19 citations · 201 across the 54 of their papers we have counts for
5 papers · 2 filters
Symmetric matrices, orthogonal Lie algebras, and Lie-Yamaguti algebras
Pilar Benito, Murray Bremner, Sara Madariaga
On the set H_n(K) of symmetric n by n matrices over the field K we can define various binary and ternary products which endow it with the structure of a Jordan algebra or a Lie or…
Structure of the rational monoid algebra for Boolean matrices of order 3
Murray R. Bremner
We use computer algebra to study the 512-dimensional associative algebra Q B_3, the rational monoid algebra of 3 x 3 Boolean matrices. We obtain a basis for the radical in bijectio…
Dendriform analogues of Lie and Jordan triple systems
Murray R. Bremner, Sara Madariaga
We use computer algebra to determine all the multilinear polynomial identities of degree satisfied by the trilinear operations and $a \cdot (b \cdot c…
A polynomial identity for the bilinear operation in Lie-Yamaguti algebras
Murray R. Bremner
We use computer algebra to demonstrate the existence of a multilinear polynomial identity of degree 8 satisfied by the bilinear operation in every Lie-Yamaguti algebra. This identi…
Free associative algebras, noncommutative Grobner bases, and universal associative envelopes for nonassociative structures
Murray R. Bremner
These are the lecture notes from my short course of the same title at the CIMPA Research School on Associative and Nonassociative Algebras and Dialgebras: Theory and Algorithms - I…