19 citations · 201 across the 54 of their papers we have counts for
41 papers · 1 filter
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…
Associator dependent algebras and Koszul duality
Murray Bremner, Vladimir Dotsenko
We resolve a ten year old open question of Loday of describing Koszul operads that act on the algebra of octonions. In fact, we obtain the answer by solving a more general classifi…
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…
Gröbner bases and dimension formulas for ternary partially associative operads
Fatemeh Bagherzadeh, Murray Bremner
Dotsenko and Vallette discovered an extension to nonsymmetric operads of Buchberger's algorithm for Gröbner bases of polynomial ideals. In the free nonsymmetric operad with one ter…
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…
Symmetrization of Jordan dialgebras
Murray R. Bremner
A basic problem for any class of nonassociative algebras is to determine the polynomial identities satisfied by the symmetrization and the skew-symmetrization of the original produ…