Publications of Murray R. Bremner

Books

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


2. M. R. Bremner and M. V. Kochetov (translators)
   L. A. Bokut, V. N. Latyshev, I. P. Shestakov and E. I. Zelmanov (editors)
   Selected Works of A. I. Shirshov in English Translation
   Birkhauser, 2009, 242 pages
   Publisher's flyer
   Publisher's web page


3. M. R. Bremner, R. V. Moody and J. Patera
   Tables of Dominant Weight Multiplicities for Representations of Simple Lie Algebras
   Marcel Dekker, 1985, 340 pages

Preprints

1. M. R. Bremner
   A polynomial identity for the bilinear operation in a Lie-Yamaguti algebra
   (submitted 6 May 2013)


2. M. R. Bremner
   Free associative algebras, noncommutative Grobner bases, and universal associative envelopes for nonassociative structures
   Lecture notes from my short course at the CIMPA Research School at CIMAT, Guanajuato, Mexico, February 17 to March 2, 2013


3. M. R. Bremner and J. Sanchez-Ortega
   Leibniz triple systems
   Submitted 1 August 2011

Accepted papers

1. M. R. Bremner and S. Madariaga
   Dendriform analogues of Lie and Jordan triple systems
   To appear in Communications in Algebra
   (submitted 6 May 2013, accepted 17 June 2013)


2. R. Felipe-Sosa, R. Felipe, J. Sanchez-Ortega, M. R. Bremner and M. K. Kinyon
   The Cayley-Dickson process for dialgebras
   To appear in Linear and Multilinear Algebra (submitted 11 September 2012, accepted 29 March 2013)


3. 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
   To appear in Linear and Multilinear Algebra (submitted 1 December 2011, revised 24 May 2012, accepted 13 August 2012)


4. M. R. Bremner and S. Madariaga
   Polynomial identities for tangent algebras of monoassociative loops
   To appear in Communications in Algebra (submitted 25 November 2011, accepted 1 May 2012)


5. M. R. Bremner and J. Hu
   The fundamental invariants of 3 x 3 x 3 arrays
   To appear in Mathematics of Computation (submitted 13 December 2011, accepted 24 April 2012)
   Data files of the three fundamental invariants:
   invariant6.txt , invariant9.txt , invariant12.txt


6. M. R. Bremner and J. Hu
   Lie invariants in two and three variables
   To appear in Algebra Colloquium (submitted 7 July 2010, accepted 27 January 2011)

Published papers

1. 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)


2. 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)


3. 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)


4. 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)


5. 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)


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


7. 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)


8. 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)


9. 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)


10. 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)


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


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


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


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


15. 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)


16. M. R. Bremner
    On the definition of quasi-Jordan algebra
    Communications in Algebra 38 (2010) 4695-4704


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


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


19. 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
    Alternating quaternary algebra structures on irreducible representations of sl(2,C) (longer version with tables)


20. 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


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


22. 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


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


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


25. 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. Edited by V. Futorny, V. Kac, I. Kashuba and E. Zelmanov.
    Proceedings of the Conference on Algebras, Representations and Applications (Maresias, Sao Paulo, Brazil, August 2007) in Honor of Ivan Shestakov's 60th Birthday.


26. 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


27. M. R. Bremner and L. A. Peresi
    Classification of trilinear operations
    Communications in Algebra 35 (2007) 2932-2959
    Errata for the published version: On page 2944, replace identity (23) by the following identity: [a,[b,c,d],e] = [[a,b,e],c,d] + [b,[a,c,e],d] + [b,c,[a,d,e]]. On page 2951, line -5, replace "all q" by "q = 1".


28. 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.
    


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


30. M. R. Bremner, L. I. Murakami and I. P. Shestakov
    Nonassociative algebras
    Chapter 69 of Handbook of Linear Algebra, Chapman & Hall / CRC, 2007
    Handbook of Linear Algebra has been recognized as an Outstanding Academic Title by Choice Magazine, published by the Association of College and Research Libraries. Further information


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


32. 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


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


34. 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, Proceedings of the Fifth International Conference (27 July - 2 August 2003, Oaxtepec, Morelos, Mexico) Chapman & Hall / CRC (2006) ISBN 0-8247-2669-3.


35. 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, edited by Ilias S. Kotsireas, published by Waterloo Maple Inc., ISBN 1-894511-85-9


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


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


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


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


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


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


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


43. 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


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


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


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


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


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


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


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


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


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


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


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


55. 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


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


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


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


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


60. M. R. Bremner
    Fast computation of weight multiplicities
    Journal of Symbolic Computation 2 (1986) 357-363

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

Published translations

1. M. R. Bremner and M. V. Kochetov (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, Proceedings of the Fifth International Conference (27 July - 2 August 2003, Oaxtepec, Morelos, Mexico) Chapman & Hall / CRC (2006) ISBN 0-8247-2669-3.


2. M. R. Bremner and N. P. 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, Proceedings of the Fifth International Conference (27 July - 2 August 2003, Oaxtepec, Morelos, Mexico) Chapman & Hall / CRC (2006) ISBN 0-8247-2669-3.