Publications of Murray Bremner

Scroll down below for books, submitted papers, accepted papers, published papers, translations, slides, and theses.

Books
  1. Murray Bremner, Vladimir Dotsenko
    Algebraic Operads: An Algorithmic Companion
    Chapman & Hall / CRC Press, 2016, 365 pages
    Publisher's web page
    PDF (version 0.99)

  2. Murray Bremner
    Lattice Basis Reduction: An Introduction to the LLL Algorithm and Its Applications
    CRC Press, 2012, 316 pages
    Publisher's web page

  3. Murray Bremner, Mikhail Kochetov (translators)
    L. A. Bokut, V. N. Latyshev, I. P. Shestakov, E. I. Zelmanov (editors)
    Selected Works of A. I. Shirshov in English Translation
    Birkhauser, Basel, 2009, 242 pages
    Publisher's web page

  4. Murray Bremner, Robert Moody, Jiri Patera
    Tables of Dominant Weight Multiplicities for Representations of Simple Lie Algebras
    Marcel Dekker, 1985, 340 pages
    ABE Books web page
Submitted papers
  1. Murray Bremner, Vladimir Dotsenko
    Distributive laws between the operads Lie and Com
    (submitted 11 December 2019)
    arXiv:1912.05519

  2. Gary Au, Fatemeh Bagherzadeh, Murray Bremner
    Enumeration and asymptotic formulas for rectangular partitions of the hypercube
    (submitted 3 March 2019)
    arXiv:1903.00813

  3. Murray R. Bremner, Juana Sánchez-Ortega
    Higher polynomial identities for mutations of associative algebras
    (submitted 13 December 2018)
    arXiv:1812.05481

  4. Murray R. Bremner, Juana Sánchez-Ortega
    Self-dual nonsymmetric operads with two binary operations
    (submitted 7 June 2016)
    arXiv:1606.01982
Accepted papers
  1. Murray Bremner, Vladimir Dotsenko
    Distributive laws between the operads Lie and Com: Extended abstract
    To appear in Proceedings of Maple Conference 2019, in the Springer series Communications in Computer and Information Science

  2. Fatemeh Bagherzadeh, Murray Bremner
    Gröbner bases and dimension formulas for ternary partially associative operads
    To appear in Proceedings of the International Workshop on Leavitt Path Algebras and K-Theory in the Indian Statistical Institute Book Series published by Springer.
    (submitted 31 July 2018, accepted 2 April 2019)
    arXiv:1810.04042
Published papers
  1. Fatemeh Bagherzadeh, Murray Bremner
    Operadic approach to cohomology of associative triple and N-tuple systems
    Glasgow Mathematical Journal. Published online by Cambridge University Press: 14 November 2019
    (submitted 10 December 2018, accepted 9 October 2019)
    arXiv:1812.03947

  2. Murray Bremner, Martin Markl
    Distributive laws between the Three Graces
    Theory and Applications of Categories Vol. 34, 2019, No. 41, pp 1317-1342
    (submitted 21 September 2018, accepted 28 October 2019)
    arXiv:1809.08191

  3. Murray Bremner
    Symmetrization of Jordan dialgebras
    Nonassociative Mathematics and its Applications
    Proceedings of the Fourth Mile High Conference on Nonassociative Mathematics (July 29–August 5, 2017, University of Denver, Denver, Colorado)
    Contemporary Mathematics, Volume 721 (2019), pages 29-42
    (submitted 31 January 2018, accepted 1 May 2018)
    arXiv:1802.00039

  4. Murray Bremner, Vladimir Dotsenko
    Boardman-Vogt tensor products of absolutely free operads
    Proceedings of the Royal Society of Edinburgh, Section A, Mathematics
    (submitted 12 May 2017, accepted 25 July 2017, published online 26 January 2019)
    arXiv:1705.04573

  5. Murray R. Bremner, Hader A. Elgendy
    Special identities for comtrans algebras
    Linear and Multilinear Algebra
    (submitted 26 June 2018, accepted 3 October 2018, published online 24 October 2018)
    arxiv:1806.10204

  6. Fatemeh Bagherzadeh, Murray Bremner
    Commutativity in double interchange semigroups
    Applied Categorical Structures (December 2018, Volume 26, Issue 6, pp 1185–1210)
    (submitted 14 June 2017, accepted 12 May 2018, published online 22 June 2018)
    arXiv:1706.04693

  7. Murray Bremner
    On tortkara triple systems
    Communications in Algebra 46, 6 (2018) 2396-2404
    (submitted 12 June 2017, accepted 4 September 2017)
    arXiv:1706.03748

  8. Murray Bremner, Vladimir Dotsenko
    Classification of regular parametrized one-relation operads
    Canadian Journal of Mathematics 69 (2017), no. 5, 992–1035
    (submitted 23 July 2015, accepted 24 May 2017)
    arXiv:1507.06372

  9. Fatemeh Bagherzadeh, Murray Bremner, Sara Madariaga
    Jordan trialgebras and post-Jordan algebras
    Journal of Algebra 486 (2017) 360–395
    (submitted 3 November 2016, accepted 29 April 2017)
    arXiv:1611.01214

  10. Murray Bremner, Juana Sánchez-Ortega
    Quadratic nonsymmetric quaternary operads
    Linear and Multilinear Algebra 65, 8 (2017) 1683-1703
    (submitted 9 December 2015, accepted 22 October 2016)
    arXiv:1512.02880

  11. Murray Bremner, Sara Madariaga, Luiz A. Peresi
    Structure theory for the group algebra of the symmetric group, with applications to polynomial identities for the octonions
    Commentationes Mathematicae Universitatis Carolinae 57, 4 (2016) 413-452
    (submitted 14 July 2015, accepted 7 October 2016)
    arXiv:1407.3810

  12. Murray Bremner
    One-parameter deformations of the diassociative and dendriform operads
    Linear and Multilinear Algebra 65, 2 (2017) 341-350
    (submitted 18 February 2016, accepted 25 April 2016)
    arXiv:1602.06026

  13. Murray Bremner, Sara Madariaga
    Lie and Jordan products in interchange algebras
    Communications in Algebra 44 (2016) 3485-3508
    (submitted 13 August 2014, accepted 14 July 2015)
    arXiv:1408.3069

  14. Murray Bremner, Sara Madariaga
    Permutation of elements in double semigroups
    Semigroup Forum 92, 2 (2016) 335-360
    (submitted 12 May 2014, accepted 12 March 2015)
    arXiv:1405.2889

  15. Pilar Benito, Murray Bremner, Sara Madariaga
    Symmetric matrices, orthogonal Lie algebras, and Lie-Yamaguti algebras
    Linear and Multilinear Algebra 63 (2015), no. 6, 1257–1281
    (submitted 17 December 2013, accepted 25 May 2014)
    arXiv:1312.5008

  16. M. R. Bremner
    A polynomial identity for the bilinear operation in a Lie-Yamaguti algebra
    Linear and Multilinear Algebra 62, 12 (2014) 1671-1682
    (submitted 6 May 2013, accepted 30 August 2013)
    arXiv:1305.1391

  17. M. R. Bremner
    Free associative algebras, noncommutative Grobner bases, and universal associative envelopes for nonassociative structures
    CMUC: Comment. Math. Univ. Carolin. 55, 3 (2014) 341-379
    (submitted 31 August 2013, accepted 5 January 2014)
    arXiv:1303.0920

  18. Murray Bremner, Jiaxiong Hu, and Luke Oeding
    The 3 x 3 x 3 hyperdeterminant as a polynomial in the fundamental invariants for SL(3,C) x SL(3,C) x SL(3,C)
    Mathematics in Computer Science 8, 2 (2014) 147-156
    (submitted 11 October 2013, accepted 17 February 2014)
    arXiv:1310.3257

  19. Murray Bremner and Sara Madariaga
    Jordan quadruple systems
    Journal of Algebra 412 (2014) 51-86
    (submitted 20 February 2014, accepted 2 May 2014)
    arXiv:1402.5152

  20. M. R. Bremner
    Structure of the rational monoid algebra for Boolean matrices of order 3
    Linear Algebra and Its Applications 449 (2104) 381-401
    (submitted 8 July 2013, accepted 18 February 2014)
    arXiv:1307.2161

  21. M. R. Bremner and J. Sanchez-Ortega
    Leibniz triple systems
    Communications in Contemporary Mathematics 16, 1350051 (2014) [19 pages]
    (submitted 1 August 2011, accepted 17 September 2013)
    arXiv:1106.5033

  22. M. R. Bremner and S. Madariaga
    Dendriform analogues of Lie and Jordan triple systems
    Communications in Algebra 42 (2014) 4696-4711
    (submitted 6 May 2013, accepted 17 June 2013)
    arXiv:1305.1389

  23. R. Felipe-Sosa, R. Felipe, J. Sanchez-Ortega, M. R. Bremner and M. K. Kinyon
    The Cayley-Dickson process for dialgebras
    Linear and Multilinear Algebra 62 (2014) 6, 811-830
    (submitted 11 September 2012, accepted 29 March 2013)
    arXiv:1209.2645

  24. M. R. Bremner and J. Hu
    Lie invariants in two and three variables
    Algebra Colloquium 21, 1 (2014) 96-116
    (submitted 7 July 2010, accepted 27 January 2011)
    arXiv:1008.2380

  25. M. R. Bremner and S. Madariaga
    Polynomial identities for tangent algebras of monoassociative loops
    Communications in Algebra 42, 1 (2014) 203-227
    (submitted 25 November 2011, accepted 1 May 2012)
    arXiv:1111.6113

  26. M. R. Bremner and J. Hu
    The fundamental invariants of 3 x 3 x 3 arrays
    Mathematics of Computation 82, 284 (2013) 2421-2438
    (submitted 13 December 2011, accepted 24 April 2012)
    Data files of the three fundamental invariants: invariant6.txt , invariant9.txt , invariant12.txt
    arXiv:1112.2949

  27. M. R. Bremner and S. G. Stavrou
    Canonical forms of 2 x 2 x 2 and 2 x 2 x 2 x 2 arrays over F_2 and F_3
    Linear and Multilinear Algebra 61, 7 (2013) 986-997
    (submitted 1 December 2011, revised 24 May 2012, accepted 13 August 2012)
    arXiv:1112.0298

  28. M. R. Bremner and S. Madariaga
    Special identities for the pre-Jordan product in the free dendriform algebra
    Linear Algebra and Its Applications 439, 2 (2013) 435-454
    (submitted 21 December 2012, accepted 5 March 2013)
    arXiv:1212.5631

  29. M. R. Bremner and J. Hu
    On Kruskal's theorem that every 3 x 3 x 3 array has rank at most 5
    Linear Algebra snd Its Applications 439, 2 (2013) 401-421
    (submitted 6 September 2012, accepted 16 March 2013)
    arXiv:1209.1553

  30. M. R. Bremner and L. A. Peresi
    Higher identities for the ternary commutator
    Journal of Physics A: Mathematical and Theoretical 45 (2012) 505201 (12 pp)
    (submitted 26 July 2012, accepted 2 November 2012, published online 21 November 2012)
    arXiv:1207.6312

  31. M. R. Bremner, L. A. Peresi, and J. Sanchez-Ortega
    Malcev dialgebras
    Linear and Multilinear Algebra 60 (2012) 1125-1141
    (submitted 1 August 2011, accepted 17 December 2011)
    arXiv:1108.0586

  32. M. R. Bremner
    A hyperdeterminant for 2 x 2 x 3 arrays
    Linear and Multilinear Algebra 60 (2012) 921-932
    (submitted 14 June 2011, accepted 19 October 2011)
    arXiv:1106.2988

  33. M. R. Bremner
    Algebras, dialgebras, and polynomial identities
    Serdica Mathematical Journal 38 (2012) 91-136
    (submitted 16 January 2012, accepted 22 June 2012)
    arXiv:1201.3379

  34. H. A. Elgendy and M. R. Bremner
    Universal associative envelopes of (n+1)-dimensional n-Lie algebras
    Communications in Algebra 40 (2012) 1827-1842
    (submitted 9 August 2010, accepted 24 January 2011)
    arXiv:1008.1987

  35. M. R. Bremner, M. G. Bickis and M. Soltanifar
    Cayley's hyperdeterminant: a combinatorial approach via representation theory
    Linear Algebra and its Applications 437 (2012) 94-112
    (submitted 24 June 2011, accepted 27 January 2012)
    arXiv:1106.5068

  36. M. R. Bremner and A. Douglas
    The simple non-Lie Malcev algebra as a Lie-Yamaguti algebra
    Journal of Algebra 358 (2012) 269-291
    (submitted 21 August 2011, accepted 27 February 2012)
    arXiv:1108.4202

  37. M. R. Bremner, R. Felipe and J. Sanchez-Ortega
    Jordan triple disystems
    Computers and Mathematics with Applications 63 (2012) 1039-1055
    (submitted 26 April 2011, accepted 2 December 2011)
    arXiv:1105.5475

  38. M. R. Bremner
    ``Matrices'', article in Encyclopedia of Mathematics and Society
    Salem Press, 2011

  39. M. V. Tvalavadze and M. R. Bremner
    Enveloping algebras of solvable Malcev algebras of dimension five
    Communications in Algebra 39 (2011) 2816-2837
    arXiv:1008.1994

  40. M. R. Bremner and L. A. Peresi
    Special identities for quasi-Jordan algebras
    Communications in Algebra 39 (2011) 2313-2337
    arXiv:1008.2723

  41. M. R. Bremner
    How to compute the Wedderburn decomposition of a finite-dimensional associative algebra
    Groups, Complexity and Cryptology 3 (2011) 47-66
    arXiv:/1008.2006

  42. M. R. Bremner and J. Sanchez Ortega
    The partially alternating ternary sum in an associative dialgebra
    Journal of Physics A: Mathematical and Theoretical 43 (2010) 455215 (18 pages)
    arXiv:/1008.2721

  43. M. R. Bremner
    On the definition of quasi-Jordan algebra
    Communications in Algebra 38 (2010) 4695-4704
    arXiv:/1008.2009

  44. M. R. Bremner
    Polynomial identities for ternary intermolecular recombination
    Discrete and Continuous Dynamical Systems, Series S 4 (2011) 1387-1399
    arXiv:/1008.2014

  45. M. R. Bremner and M. El Bachraoui
    On the semigroup algebra of binary relations
    Communications in Algebra 38 (2010) 3499-3505

  46. M. R. Bremner and H. A. Elgendy
    Alternating quaternary algebra structures on irreducible representations of sl(2,C)
    Linear Algebra and its Applications 433 (2010) 1686-1705
    arXiv:/1008.1998

  47. M. R. Bremner, I. R. Hentzel, L. A. Peresi, M. V. Tvalavadze and H. Usefi
    Enveloping algebras of Malcev algebras
    Commentationes Mathematicae Universitatis Carolinae 51 (2010) 157-174
    arXiv:/1008.2388

  48. M. R. Bremner and H. Usefi
    Enveloping algebras of the nilpotent Malcev algebra of dimension five
    Algebras and Representation Theory 13 (2010) 407-425
    arXiv:/1008.2728

  49. M. R. Bremner, Y. F. Piao and S. W. Richards
    Polynomial identities for Bernstein algebras of simple Mendelian inheritance
    Communications in Algebra 37 (2009) 3438-3455

  50. M. R. Bremner and L. A. Peresi
    Nonhomogeneous subalgebras of Lie and special Jordan superalgebras
    Journal of Algebra 322 (2009) 2000-2026

  51. M. R. Bremner and L. A. Peresi
    Polynomial identities for the ternary cyclic sum
    Linear and Multilinear Algebra 57 (2009) 595-608

  52. M. R. Bremner, I. R. Hentzel, L. A. Peresi and H. Usefi
    Universal enveloping algebras of the four-dimensional Malcev algebra
    Pages 73-90, Volume 483, Contemporary Mathematics, American Mathematical Society.

  53. M. R. Bremner and L. A. Peresi
    An application of lattice basis reduction to polynomial identities for algebraic structures
    Linear Algebra and its Applications 430 (2009) 642-659

  54. M. R. Bremner and L. A. Peresi
    Classification of trilinear operations
    Communications in Algebra 35 (2007) 2932-2959

  55. M. R. Bremner, M. J. Hancock and Y. F. Piao
    Nonassociative structures on polynomial algebras arising from bio-operations on formal languages
    Proceedings of ISSAC'07, Waterloo, Ontario, Canada, July 29 to August 1, 2007.

  56. M. R. Bremner
    An algebra which is power associative but not strictly power associative
    Communications in Algebra 35 (2007) 261-264

  57. M. R. Bremner, L. I. Murakami and I. P. Shestakov
    Nonassociative algebras
    Chapter 69 of Handbook of Linear Algebra, Chapman & Hall / CRC, 2007

  58. M. R. Bremner
    Jordan algebras arising from intermolecular recombination
    Communications in Computer Algebra (SIGSAM Bulletin) 39 (2005) 106-117.

  59. M. R. Bremner and I. R. Hentzel
    Identities relating the Jordan product and the associator in the free nonassociative algebra
    Journal of Algebra and its Applications 5 (2006) 77-88

  60. M. R. Bremner and L. A. Peresi
    Ternary analogues of Lie and Malcev algebras
    Linear Algebra and its Applications 414 (2006) 1-18

  61. M. R. Bremner and I. R. Hentzel
    Alternating triple systems with simple Lie algebras of derivations
    Non-Associative Algebra and its Applications, pages 55-82, Chapman & Hall / CRC (2006) ISBN 0-8247-2669-3.

  62. M. R. Bremner
    DNA computing, insertion of words and left-symmetric algebras
    Proceedings of Maple Conference 2005 (July 17-20, 2005, Waterloo, Canada), pages 229-242, ISBN 1-894511-85-9.

  63. M. R. Bremner, I. R. Hentzel and L. A. Peresi
    Dimension formulas for the free nonassociative algebra
    Communications in Algebra 33 (2005) 4063-4081

  64. M. R. Bremner, I. R. Hentzel and L. A. Peresi
    Dimension formulas for the free nonassociative algebra
    Resenhas IME-USP 6 (2004) 141-151 (Resenhas do Instituto de Matematica e Estatistica da Universidade de Sao Paulo)

  65. M. R. Bremner and I. R. Hentzel
    Invariant nonassociative algebra structures on irreducible representations of simple Lie algebras
    Experimental Mathematics 13 (2004) 231-256

  66. M. R. Bremner and I. R. Hentzel
    Identities for algebras of matrices over the octonions
    Journal of Algebra 277 (2004) 73-95

  67. M. R. Bremner
    Additive structure of free left-symmetric and assosymmetric rings
    International Journal of Mathematics, Game Theory and Algebra 12 (2002) 23-37

  68. M. R. Bremner and I. R. Hentzel
    Identities for the associator in alternative algebras
    Journal of Symbolic Computation 33 (2002) 255-273

  69. M. R. Bremner
    New ternary versions of Jordan algebras
    Algebra Colloquium 8 (2001) 11-24

  70. M. R. Bremner and I. R. Hentzel
    Identities for algebras obtained from the Cayley-Dickson process
    Communications in Algebra 29 (2001) 3523-3534

  71. M. R. Bremner and I. R. Hentzel
    Identities for generalized Lie and Jordan products on totally associative triple systems
    Journal of Algebra 231 (2000) 387-405

  72. M. R. Bremner
    On free partially associative triple systems
    Communications in Algebra 28 (2000) 2131-2145

  73. M. R. Bremner
    Quantum octonions
    Communications in Algebra 27 (1999) 2809-2831

  74. M. R. Bremner
    On the Z-module structure of a free semialternative ring
    Communications in Algebra 27 (1999) 1951-1965

  75. M. R. Bremner
    Lie invariants of degree ten
    International Journal of Mathematics, Game Theory and Algebra 8 (1998) 115-122

  76. M. R. Bremner
    Identities for the ternary commutator
    Journal of Algebra 206 (1998) 615-623

  77. M. R. Bremner
    Quantum deformations of simple Lie algebras
    Canadian Mathematical Bulletin 40 (1997) 143-148

  78. M. R. Bremner
    Varieties of anticommutative n-ary algebras
    Journal of Algebra 191 (1997) 76-88

  79. M. R. Bremner
    Classifying varieties of anti-commutative algebras
    Nova Journal of Mathematics, Game Theory and Algebra 4 (1996) 119-127

  80. M. R. Bremner
    Four-point affine Lie algebras
    Proceedings of the American Mathematical Society 123 (1995) 1981-1989

  81. M. R. Bremner
    Universal central extensions of elliptic affine Lie algebras
    Journal of Mathematical Physics 35 (1994) 6685-6692

  82. M. R. Bremner
    Generalized Kac-Moody Lie algebras over localizations of the polynomial ring in one variable
    Canadian Mathematical Bulletin 37 (1994) 21-28

  83. M. R. Bremner
    Structure of the Lie algebra of polynomial vector fields on the Riemann sphere with three punctures
    Journal of Mathematical Physics 32 (1991) 1607-1608

  84. M. R. Bremner
    On a Lie algebra of vector fields on a complex torus
    Journal of Mathematical Physics 31 (1990) 2033-2034

  85. M. R. Bremner
    Modular invariant Virasoro modules and elliptic curves
    Letters in Mathematical Physics 20 (1990) 113-123

  86. M. R. Bremner
    Tensor products of unitary super-Virasoro modules with central charge 7/10
    Canadian Journal of Mathematics 42 (1990) 561-574

  87. M. R. Bremner
    Tensor products of unitarizable representations of the Virasoro algebra with central charge 1/2
    Communications in Algebra 16 (1988) 1513-1523

  88. M. R. Bremner
    Fast computation of weight multiplicities
    Journal of Symbolic Computation 2 (1986) 357-363
Translations
  1. Murray Bremner (translator)
    The renaissance of operads (by Jean-Louis Loday)
    Unpublished
    PDF

  2. Murray Bremner, Mikhail Kotchetov (translators)
    The Dniester Notebook: Unsolved Problems in the Theory of Rings and Modules
    Fourth edition, 1993, compiled by V. T. Filippov, V. K. Kharchenko and I. P. Shestakov
    Non-Associative Algebra and its Applications, pages 461-516, Chapman & Hall / CRC (2006) ISBN 0-8247-2669-3
    PDF

  3. Murray Bremner, Natalia Fomenko (translators)
    Some problems in the theory of rings that are nearly associative by A. I. Shirshov
    Non-Associative Algebra and its Applications, pages 441-459, Chapman & Hall / CRC (2006) ISBN 0-8247-2669-3
    PDF
Slides
  1. Murray Bremner
    An Introduction to the Narayana Numbers
    1 March 2018, Math and Stats Society, University of Saskatchewan
    PDF

  2. Murray Bremner
    What is ... higher-dimensional algebra?
    1 March 2018, Math and Stats Society, University of Saskatchewan
    PDF

  3. Murray Bremner
    A constructive approach to the structure theory for the group algebra of the symmetric group S_n
    13-24 November 2017, Suleyman Demirel University, Kaskelen (near Almaty), Kazakhstan
    PDF

  4. Murray Bremner
    Associative and nonassociative structures arising from algebraic operads
    CIMPA Research School, 7-19 August 2017, "Associative and Nonassociative Algebras", Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Akademgorodok, Novosibirsk, Russia
    PDF

  5. Fatemeh Bagherzadeh and Murray Bremner
    Commutativity in double interchange semigroups
    CT 2017: Category Theory 2017, University of British Columbia, Vancouver, Canada, 16-22 July 2017
    PDF

  6. Murray Bremner
    Classification of nonsymmetric operads using computational linear and commutative algebra
    Nonassociative Algebra and Lie Theory, Mexico City, 27 February to 3 March 2017
    PDF

  7. Murray Bremner, Vladimir Dotsenko
    Classification of regular parametrized one-relation operads
    CMS Summer Meeting, Session on Representation Theory, University of Alberta, Edmonton, 24–27 June 2016
    PDF

  8. Murray Bremner
    Binary-ternary Wedderburn-Etherington numbers (with applications and generalizations)
    ACMES 2, Western University, London, Ontario, Canada, 12-15 May 2016
    PDF

  9. Murray Bremner
    Linear algebra over polynomial rings
    Trinity College Dublin, 29 October 2015
    PDF

  10. Murray Bremner
    Catalan numbers
    University of Cape Town, 30 November 2015
    PDF
Theses
  1. M. R. Bremner
    On Tensor Products of Modules over the Virasoro Algebra
    Ph.D. Thesis, Department of Mathematics, Yale University, 1989

  2. M. R. Bremner
    Computation of Weight Multiplicities in Representations of Lie Algebras
    M.Comp.Sc. Thesis, Department of Computer Science, Concordia University, 1984