2 citations · 4 across the 8 of their papers we have counts for
8 papers
Poisson triple systems
Murray Bremner, Hader Elgendy
We introduce Poisson triple systems, which are vector spaces with 3 trilinear operations satisfying 9 polynomial identities of degree 5. We show that every Poisson triple system ha…
On the irreducible representations of the Jordan triple system of matrices
Hader A. Elgendy
Let $\mathcal{J}_{\field}$ be the Jordan triple system of all (; rectangular matrices over a field $\field$ of characteristic 0 with the triple prod…
A new classification of algebraic identities for linear operators on associative algebras
Murray R. Bremner, Hader A. Elgendy
We introduce a new approach to the classification of operator identities, based on basic concepts from the theory of algebraic operads together with computational commutative algeb…
Special Identities for Comtrans Algebras
Murray R. Bremner, Hader A. Elgendy
Comtrans algebras, arising in web geometry, have two trilinear operations, commutator and translator. We determine a Gröbner basis for the comtrans operad, and state a conjecture o…
The universal Associative envelope of the anti-Jordan triple system of matrices
Hader A. Elgendy
We show that the universal associative enveloping algebra of the simple anti-Jordan triple system of all matrices over an algebraically closed field of cha…
Universal associative envelopes of nonassociative triple systems
Hader A. Elgendy
We construct universal associative envelopes for the nonassociative triple systems arising from the trilinear operations of Bremner and Peresi applied to the 2-dimensional simple a…
Alternating quaternary algebra structures on irreducible representations of sl(2,C)
Murray R. Bremner, Hader A. elgendy
We determine the multiplicity of the irreducible representation V(n) of the simple Lie algebra sl(2,C) as a direct summand of its fourth exterior power . The multiplicity…
Universal associative envelopes of (n+1)-dimensional n-Lie algebras
Murray R. Bremner, Hader A. Elgendy
For n even, we prove Pozhidaev's conjecture on the existence of associative enveloping algebras for simple n-Lie algebras. More generally, for n even and any (n+1)-dimensional n-Li…