Publications of Murray R. Bremner

Books

1. Lattice Basis Reduction: An Introduction to the LLL Algorithm and Its Applications
   M. R. Bremner
   CRC Press, 2012 (published August 2011)
   Publisher's flyer in PDF format
   Publisher's web page for the book


2. Selected Works of A. I. Shirshov
   M. R. Bremner and M. V. Kochetov (translators)
   L. A. Bokut, V. N. Latyshev, I. P. Shestakov and E. I. Zelmanov (editors)
   Birkhauser, Basel-Boston-Berlin, 2009, 242 pages


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

Preprints

1. M. R. Bremner
   Algebras, dialgebras, and polynomial identities
   Submitted 16 January 2012


2. M. R. Bremner and J. Hu
   The fundamental invariants of 3 x 3 x 3 arrays
   Submitted 13 December 2011


3. M. R. Bremner and S. G. Stavrou
   Ranks of 0-1 arrays of size 2 x 2 x 2 and 2 x 2 x 2 x 2
   Submitted 1 December 2011


4. M. R. Bremner
   The hyperdeterminant of 3 x 3 x 2 arrays, and the simplest invariant of 4 x 4 x 2 arrays
   Submitted 25 November 2011


5. M. R. Bremner and S. Madariaga
   Polynomial identities for tangent algebras of monoassociative loops
   Submitted 25 November 2011


6. M. R. Bremner and A. Douglas
   The simple non-Lie Malcev algebra as a Lie-Yamaguti algebra
   Submitted 21 August 2011


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

Accepted papers

1. M. R. Bremner, M. G. Bickis, and M. Soltanifar
   Cayley's hyperdeterminant: a combinatorial approach via representation theory
   To appear in Linear Algebra and its Applications (submitted 24 June 2011, revised 26 January 2012, accepted 27 January 2012)


2. M. R. Bremner, L. A. Peresi, and J. Sanchez-Ortega
   Malcev dialgebras
   To appear in Linear and Multilinear Algebra (submitted 1 August 2011, accepted 17 December 2011)


3. M. R. Bremner, R. Felipe and J. Sanchez-Ortega
   Jordan triple disystems
   To appear in Computers and Mathematics with Applications (submitted 26 April 2011, accepted 2 December 2011)


4. M. R. Bremner
   A hyperdeterminant for 2 x 2 x 3 arrays
   To appear in Linear and Multilinear Algebra (submitted 14 June 2011, accepted 19 October 2011)


5. 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)


6. H. A. Elgendy and M. R. Bremner
   Universal associative envelopes of (n+1)-dimensional n-Lie algebras
   To appear in Communications in Algebra (submitted 9 August 2010, accepted 24 January 2011)

Published papers

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


2. M. V. Tvalavadze and M. R. Bremner
   Enveloping algebras of solvable Malcev algebras of dimension five
   Communications in Algebra 39:8 (2011) 2816-2837


3. M. R. Bremner and L. A. Peresi
   Special identities for quasi-Jordan algebras
   Communications in Algebra 39:7 (2011) 2313-2337


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


5. M. R. Bremner and J. Sanchez Ortega
   The partially alternating ternary sum in an associative dialgebra
   J. Phys. A: Math. Theor. 43 (2010) 455215 (18 pages)


6. M. R. Bremner
   On the definition of quasi-Jordan algebra
   Communications in Algebra 38, 12 (2010) 4695-4704


7. M. R. Bremner
   Polynomial identities for ternary intermolecular recombination
   Discrete and Continuous Dynamical Systems, Series S, Volume 4, Number 6, December 2011, Pages 1387-1399


8. M. R. Bremner and M. El Bachraoui
   On the semigroup algebra of binary relations
   Communications in Algebra 38, 9 (2010) 3499-3505 (accepted 24 March 2009)


9. M. R. Bremner and H. A. Elgendy
   Alternating quaternary algebra structures on irreducible representations of sl(2,C)
   Linear Algebra and its Applications, Volume 433, Issues 8-10, 15 December 2010, Pages 1686-1705 (accepted 9 June 2010)
   Alternating quaternary algebra structures on irreducible representations of sl(2,C) (longer version with tables)


10. M. R. Bremner, I. R. Hentzel, L. A. Peresi, M. V. Tvalavadze and H. Usefi
    Enveloping algebras of Malcev algebras
    CMUC - Commentationes Mathematicae Universitatis Carolinae 51, 2 (2010) 157-174 (accepted 8 February 2010)


11. M. R. Bremner and H. Usefi
    Enveloping algebras of the nilpotent Malcev algebra of dimension five
    Algebras and Representation Theory, Volume 13, Number 4 (August 2010) 407-425 (accepted 24 June 2008, published online 17 February 2009)


12. 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 (accepted 16 September 2008)


13. M. R. Bremner and L. A. Peresi
    Nonhomogeneous subalgebras of Lie and special Jordan superalgebras
    Journal of Algebra 322 (2009) 2000-2026 (accepted 24 June 2009)


14. M. R. Bremner and L. A. Peresi
    Polynomial identities for the ternary cyclic sum
    Linear and Multilinear Algebra 57 (2009) 595-608 (accepted 9 May 2008)


15. 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.


16. 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) no. 2-3, 642-659


17. 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".


18. 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.
    


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


20. 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


21. M. R. Bremner
    Jordan algebras arising from intermolecular recombination
    Communications in Computer Algebra (SIGSAM Bulletin): Formally Reviewed Article. Volume 39, Number 4, December 2005, Issue 154, pages 106-117.


22. 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


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


24. 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.


25. 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


26. M. R. Bremner, I. R. Hentzel and L. A. Peresi
    Dimension formulas for the free nonassociative algebra
    Communications in Algebra 33 (2005), no. 11, 4063--4081
    Dimension formulas for the free nonassociative algebra
    Resenhas IME-USP 6 (2004), nos. 2-3, 141-151 (Resenhas do Instituto de Matematica e Estatistica da Universidade de Sao Paulo)


27. M. R. Bremner and I. R. Hentzel
    Invariant nonassociative algebra structures on irreducible representations of simple Lie algebras
    Experimental Mathematics 13 (2004), no. 2, 231-256


28. M. R. Bremner and I. R. Hentzel
    Identities for algebras of matrices over the octonions
    Journal of Algebra 277 (2004), no. 1, 73-95


29. M. R. Bremner
    Additive structure of free left-symmetric and assosymmetric rings [scanned PDF of published version]
    International Journal of Mathematics, Game Theory and Algebra 12 (2002), no. 1, 23-37


30. M. R. Bremner and I. R. Hentzel
    Identities for the associator in alternative algebras
    Journal of Symbolic Computation 33 (2002), no. 3, 255-273


31. M. R. Bremner
    New ternary versions of Jordan algebras
    Algebra Colloquium 8 (2001), no. 1, 11-24


32. M. R. Bremner and I. R. Hentzel
    Identities for algebras obtained from the Cayley-Dickson process
    Communications in Algebra 29 (2001), no. 8, 3523-3534


33. M. R. Bremner and I. R. Hentzel
    Identities for generalized Lie and Jordan products on totally associative triple systems
    Journal of Algebra 231 (2000), no. 1, 387-405


34. M. R. Bremner
    On free partially associative triple systems
    Communications in Algebra 28 (2000), no. 4, 2131-2145


35. M. R. Bremner
    Quantum octonions
    Communications in Algebra 27 (1999), no. 6, 2809-2831


36. M. R. Bremner
    On the Z-module structure of a free semialternative ring
    Communications in Algebra 27 (1999), no. 4, 1951-1965


37. M. R. Bremner
    Lie invariants of degree ten
    International Journal of Mathematics, Game Theory and Algebra 8 (1998), nos. 2-3, 115-122


38. M. R. Bremner
    Identities for the ternary commutator
    Journal of Algebra 206 (1998), no. 2, 615-623


39. M. R. Bremner
    Quantum deformations of simple Lie algebras
    Canadian Mathematical Bulletin 40 (1997), no. 2, 143-148


40. M. R. Bremner
    Varieties of anticommutative n-ary algebras
    Journal of Algebra 191 (1997), no. 1, 76-88


41. M. R. Bremner
    Classifying varieties of anti-commutative algebras
    Nova Journal of Mathematics, Game Theory and Algebra 4 (1996), no. 2, 119-127


42. M. R. Bremner
    Four-point affine Lie algebras
    Proceedings of the American Mathematical Society 123 (1995), no. 7, 1981-1989


43. M. R. Bremner
    Universal central extensions of elliptic affine Lie algebras
    Journal of Mathematical Physics 35 (1994), no. 12, 6685-6692


44. M. R. Bremner
    Generalized Kac-Moody Lie algebras over localizations of the polynomial ring in one variable
    Canadian Mathematical Bulletin 37 (1994), no. 1, 21-28


45. 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), no. 6, 1607-1608


46. M. R. Bremner
    On a Lie algebra of vector fields on a complex torus
    Journal of Mathematical Physics 31 (1990), no. 8, 2033-2034


47. M. R. Bremner
    Modular invariant Virasoro modules and elliptic curves
    Letters in Mathematical Physics 20 (1990), no. 2, 113-123


48. M. R. Bremner
    Tensor products of unitary super-Virasoro modules with central charge 7/10
    Canadian Journal of Mathematics 42 (1990), no. 3, 561-574


49. M. R. Bremner
    Tensor products of unitarizable representations of the Virasoro algebra with central charge 1/2
    Communications in Algebra 16 (1988), no. 7, 1513-1523


50. M. R. Bremner
    Fast computation of weight multiplicities
    Journal of Symbolic Computation 2 (1986), no. 4, 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.