Publications of Murray Bremner
Scroll down below for books, submitted papers, accepted papers, published papers, translations, slides, and theses.
Books

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

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

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

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

Murray Bremner, Vladimir Dotsenko
Distributive laws between the operads Lie and Com
(submitted 11 December 2019)
arXiv:1912.05519

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

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

Murray R. Bremner, Juana SánchezOrtega
Selfdual nonsymmetric operads with two binary operations
(submitted 7 June 2016)
arXiv:1606.01982
Accepted papers

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

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 KTheory in the Indian Statistical Institute Book
Series published by Springer.
(submitted 31 July 2018, accepted 2 April 2019)
arXiv:1810.04042
Published papers

Fatemeh Bagherzadeh, Murray Bremner
Operadic approach to cohomology of associative triple and Ntuple systems
Glasgow Mathematical Journal.
Published online by Cambridge University Press: 14 November 2019
(submitted 10 December 2018, accepted 9 October 2019)
arXiv:1812.03947

Murray Bremner, Martin Markl
Distributive laws between the Three Graces
Theory and Applications of Categories
Vol. 34, 2019, No. 41, pp 13171342
(submitted 21 September 2018, accepted 28 October 2019)
arXiv:1809.08191

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 2942
(submitted 31 January 2018, accepted 1 May 2018)
arXiv:1802.00039

Murray Bremner, Vladimir Dotsenko
BoardmanVogt 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

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

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

Murray Bremner
On tortkara triple systems
Communications in Algebra
46, 6 (2018) 23962404
(submitted 12 June 2017, accepted 4 September 2017)
arXiv:1706.03748

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

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

Murray Bremner, Juana SánchezOrtega
Quadratic nonsymmetric quaternary operads
Linear and Multilinear Algebra
65, 8 (2017) 16831703
(submitted 9 December 2015, accepted 22 October 2016)
arXiv:1512.02880

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) 413452
(submitted 14 July 2015, accepted 7 October 2016)
arXiv:1407.3810

Murray Bremner
Oneparameter deformations of the diassociative and dendriform operads
Linear and Multilinear Algebra
65, 2 (2017) 341350
(submitted 18 February 2016, accepted 25 April 2016)
arXiv:1602.06026

Murray Bremner, Sara Madariaga
Lie and Jordan products in interchange algebras
Communications in Algebra 44 (2016) 34853508
(submitted 13 August 2014, accepted 14 July 2015)
arXiv:1408.3069

Murray Bremner, Sara Madariaga
Permutation of elements in double semigroups
Semigroup Forum 92, 2 (2016) 335360
(submitted 12 May 2014, accepted 12 March 2015)
arXiv:1405.2889

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

M. R. Bremner
A polynomial identity for the bilinear operation in a LieYamaguti algebra
Linear and Multilinear Algebra 62, 12 (2014) 16711682
(submitted 6 May 2013, accepted 30 August 2013)
arXiv:1305.1391

M. R. Bremner
Free associative algebras, noncommutative Grobner bases, and universal associative envelopes for nonassociative structures
CMUC: Comment. Math. Univ. Carolin. 55, 3 (2014) 341379
(submitted 31 August 2013, accepted 5 January 2014)
arXiv:1303.0920

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) 147156
(submitted 11 October 2013, accepted 17 February 2014)
arXiv:1310.3257

Murray Bremner and Sara Madariaga
Jordan quadruple systems
Journal of Algebra
412 (2014) 5186
(submitted 20 February 2014, accepted 2 May 2014)
arXiv:1402.5152

M. R. Bremner
Structure of the rational monoid algebra for Boolean matrices of order 3
Linear Algebra and Its Applications
449 (2104) 381401
(submitted 8 July 2013, accepted 18 February 2014)
arXiv:1307.2161

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

M. R. Bremner and S. Madariaga
Dendriform analogues of Lie and Jordan triple systems
Communications in Algebra
42 (2014) 46964711
(submitted 6 May 2013, accepted 17 June 2013)
arXiv:1305.1389

R. FelipeSosa, R. Felipe, J. SanchezOrtega, M. R. Bremner and M. K. Kinyon
The CayleyDickson process for dialgebras
Linear and Multilinear Algebra
62 (2014) 6, 811830
(submitted 11 September 2012, accepted 29 March 2013)
arXiv:1209.2645

M. R. Bremner and J. Hu
Lie invariants in two and three variables
Algebra Colloquium 21, 1 (2014) 96116
(submitted 7 July 2010, accepted 27 January 2011)
arXiv:1008.2380

M. R. Bremner and S. Madariaga
Polynomial identities for tangent algebras of monoassociative loops
Communications in Algebra 42, 1 (2014) 203227
(submitted 25 November 2011, accepted 1 May 2012)
arXiv:1111.6113

M. R. Bremner and J. Hu
The fundamental invariants of 3 x 3 x 3 arrays
Mathematics of Computation 82, 284 (2013) 24212438
(submitted 13 December 2011, accepted 24 April 2012)
Data files of the three fundamental invariants:
invariant6.txt
,
invariant9.txt
,
invariant12.txt
arXiv:1112.2949

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) 986997
(submitted 1 December 2011, revised 24 May 2012, accepted 13 August 2012)
arXiv:1112.0298

M. R. Bremner and S. Madariaga
Special identities for the preJordan product in the free dendriform algebra
Linear Algebra and Its Applications 439, 2 (2013) 435454
(submitted 21 December 2012, accepted 5 March 2013)
arXiv:1212.5631

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) 401421
(submitted 6 September 2012, accepted 16 March 2013)
arXiv:1209.1553

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

M. R. Bremner, L. A. Peresi, and J. SanchezOrtega
Malcev dialgebras
Linear and Multilinear Algebra 60 (2012) 11251141
(submitted 1 August 2011, accepted 17 December 2011)
arXiv:1108.0586

M. R. Bremner
A hyperdeterminant for 2 x 2 x 3 arrays
Linear and Multilinear Algebra 60 (2012) 921932
(submitted 14 June 2011, accepted 19 October 2011)
arXiv:1106.2988

M. R. Bremner
Algebras, dialgebras, and polynomial identities
Serdica Mathematical Journal 38 (2012) 91136
(submitted 16 January 2012, accepted 22 June 2012)
arXiv:1201.3379

H. A. Elgendy and M. R. Bremner
Universal associative envelopes of (n+1)dimensional nLie algebras
Communications in Algebra 40 (2012) 18271842
(submitted 9 August 2010, accepted 24 January 2011)
arXiv:1008.1987

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) 94112
(submitted 24 June 2011, accepted 27 January 2012)
arXiv:1106.5068

M. R. Bremner and A. Douglas
The simple nonLie Malcev algebra as a LieYamaguti algebra
Journal of Algebra 358 (2012) 269291
(submitted 21 August 2011, accepted 27 February 2012)
arXiv:1108.4202

M. R. Bremner, R. Felipe and J. SanchezOrtega
Jordan triple disystems
Computers and Mathematics with Applications 63 (2012) 10391055
(submitted 26 April 2011, accepted 2 December 2011)
arXiv:1105.5475

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

M. V. Tvalavadze and M. R. Bremner
Enveloping algebras of solvable Malcev algebras of dimension five
Communications in Algebra
39 (2011) 28162837
arXiv:1008.1994

M. R. Bremner and L. A. Peresi
Special identities for quasiJordan algebras
Communications in Algebra
39 (2011) 23132337
arXiv:1008.2723

M. R. Bremner
How to compute the Wedderburn decomposition of a finitedimensional associative algebra
Groups, Complexity and Cryptology
3 (2011) 4766
arXiv:/1008.2006

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

M. R. Bremner
On the definition of quasiJordan algebra
Communications in Algebra
38 (2010) 46954704
arXiv:/1008.2009

M. R. Bremner
Polynomial identities for ternary intermolecular recombination
Discrete and Continuous Dynamical Systems, Series S 4 (2011) 13871399
arXiv:/1008.2014

M. R. Bremner and M. El Bachraoui
On the semigroup algebra of binary relations
Communications in Algebra 38 (2010) 34993505

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) 16861705
arXiv:/1008.1998

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) 157174
arXiv:/1008.2388

M. R. Bremner and H. Usefi
Enveloping algebras of the nilpotent Malcev algebra of dimension five
Algebras and Representation Theory 13 (2010) 407425
arXiv:/1008.2728

M. R. Bremner, Y. F. Piao and S. W. Richards
Polynomial identities for Bernstein algebras of simple Mendelian inheritance
Communications in Algebra 37 (2009) 34383455

M. R. Bremner and L. A. Peresi
Nonhomogeneous subalgebras of Lie and special Jordan superalgebras
Journal of Algebra 322 (2009) 20002026

M. R. Bremner and L. A. Peresi
Polynomial identities for the ternary cyclic sum
Linear and Multilinear Algebra 57 (2009) 595608

M. R. Bremner, I. R. Hentzel, L. A. Peresi and H. Usefi
Universal enveloping algebras of the fourdimensional Malcev algebra
Pages 7390, Volume 483, Contemporary Mathematics, American Mathematical Society.

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) 642659

M. R. Bremner and L. A. Peresi
Classification of trilinear operations
Communications in Algebra
35 (2007) 29322959

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

M. R. Bremner
An algebra which is power associative but not strictly power associative
Communications in Algebra
35 (2007) 261264

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

M. R. Bremner
Jordan algebras arising from intermolecular recombination
Communications in Computer Algebra (SIGSAM Bulletin)
39 (2005) 106117.

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) 7788

M. R. Bremner and L. A. Peresi
Ternary analogues of Lie and Malcev algebras
Linear Algebra and its Applications
414 (2006) 118

M. R. Bremner and I. R. Hentzel
Alternating triple systems with simple Lie algebras of derivations
NonAssociative Algebra and its Applications, pages 5582,
Chapman & Hall / CRC (2006) ISBN 0824726693.

M. R. Bremner
DNA computing, insertion of words and leftsymmetric algebras
Proceedings of Maple Conference 2005 (July 1720, 2005, Waterloo, Canada), pages 229242, ISBN 1894511859.

M. R. Bremner, I. R. Hentzel and L. A. Peresi
Dimension formulas for the free nonassociative algebra
Communications in Algebra
33 (2005) 40634081

M. R. Bremner, I. R. Hentzel and L. A. Peresi
Dimension formulas for the free nonassociative algebra
Resenhas IMEUSP
6 (2004) 141151
(Resenhas do Instituto de Matematica e Estatistica da Universidade de Sao Paulo)

M. R. Bremner and I. R. Hentzel
Invariant nonassociative algebra structures on irreducible representations of simple Lie algebras
Experimental Mathematics
13 (2004) 231256

M. R. Bremner and I. R. Hentzel
Identities for algebras of matrices over the octonions
Journal of Algebra
277 (2004) 7395

M. R. Bremner
Additive structure of free leftsymmetric and assosymmetric rings
International Journal of Mathematics, Game Theory and Algebra
12 (2002) 2337

M. R. Bremner and I. R. Hentzel
Identities for the associator in alternative algebras
Journal of Symbolic Computation
33 (2002) 255273

M. R. Bremner
New ternary versions of Jordan algebras
Algebra Colloquium
8 (2001) 1124

M. R. Bremner and I. R. Hentzel
Identities for algebras obtained from the CayleyDickson process
Communications in Algebra
29 (2001) 35233534

M. R. Bremner and I. R. Hentzel
Identities for generalized Lie and Jordan products on totally associative triple systems
Journal of Algebra
231 (2000) 387405

M. R. Bremner
On free partially associative triple systems
Communications in Algebra
28 (2000) 21312145

M. R. Bremner
Quantum octonions
Communications in Algebra
27 (1999) 28092831

M. R. Bremner
On the Zmodule structure of a free semialternative ring
Communications in Algebra
27 (1999) 19511965

M. R. Bremner
Lie invariants of degree ten
International Journal of Mathematics, Game Theory and Algebra
8 (1998) 115122

M. R. Bremner
Identities for the ternary commutator
Journal of Algebra
206 (1998) 615623

M. R. Bremner
Quantum deformations of simple Lie algebras
Canadian Mathematical Bulletin
40 (1997) 143148

M. R. Bremner
Varieties of anticommutative nary algebras
Journal of Algebra
191 (1997) 7688

M. R. Bremner
Classifying varieties of anticommutative algebras
Nova Journal of Mathematics, Game Theory and Algebra
4 (1996) 119127

M. R. Bremner
Fourpoint affine Lie algebras
Proceedings of the American Mathematical Society
123 (1995) 19811989

M. R. Bremner
Universal central extensions of elliptic affine Lie algebras
Journal of Mathematical Physics
35 (1994) 66856692

M. R. Bremner
Generalized KacMoody Lie algebras over localizations of the polynomial ring in one variable
Canadian Mathematical Bulletin
37 (1994) 2128

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) 16071608

M. R. Bremner
On a Lie algebra of vector fields on a complex torus
Journal of Mathematical Physics
31 (1990) 20332034

M. R. Bremner
Modular invariant Virasoro modules and elliptic curves
Letters in Mathematical Physics
20 (1990) 113123

M. R. Bremner
Tensor products of unitary superVirasoro modules with central charge 7/10
Canadian Journal of Mathematics
42 (1990) 561574

M. R. Bremner
Tensor products of unitarizable representations of the Virasoro algebra with central charge 1/2
Communications in Algebra
16 (1988) 15131523

M. R. Bremner
Fast computation of weight multiplicities
Journal of Symbolic Computation
2 (1986) 357363
Translations

Murray Bremner (translator)
The renaissance of operads (by JeanLouis Loday)
Unpublished
PDF

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
NonAssociative Algebra and its Applications, pages 461516,
Chapman & Hall / CRC (2006) ISBN 0824726693
PDF

Murray Bremner, Natalia Fomenko (translators)
Some problems in the theory of rings that are nearly associative
by A. I. Shirshov
NonAssociative Algebra and its Applications, pages 441459,
Chapman & Hall / CRC (2006) ISBN 0824726693
PDF
Slides

Murray Bremner
An Introduction to the Narayana Numbers
1 March 2018, Math and Stats Society, University of Saskatchewan
PDF

Murray Bremner
What is ... higherdimensional algebra?
1 March 2018, Math and Stats Society, University of Saskatchewan
PDF

Murray Bremner
A constructive approach to the structure theory for the group algebra of the symmetric group S_n
1324 November 2017, Suleyman Demirel University, Kaskelen (near Almaty), Kazakhstan
PDF

Murray Bremner
Associative and nonassociative structures arising from algebraic operads
CIMPA Research School, 719 August 2017,
"Associative and Nonassociative Algebras",
Sobolev Institute of Mathematics,
Siberian Branch, Russian Academy of Sciences,
Akademgorodok, Novosibirsk, Russia
PDF

Fatemeh Bagherzadeh and Murray Bremner
Commutativity in double interchange semigroups
CT 2017: Category Theory 2017,
University of British Columbia,
Vancouver, Canada,
1622 July 2017
PDF

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

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

Murray Bremner
Binaryternary WedderburnEtherington numbers (with applications and generalizations)
ACMES 2, Western University, London, Ontario, Canada, 1215 May 2016
PDF

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

Murray Bremner
Catalan numbers
University of Cape Town, 30 November 2015
PDF
Theses

M. R. Bremner
On Tensor Products of Modules over the Virasoro Algebra
Ph.D. Thesis, Department of Mathematics, Yale University, 1989

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