19 citations · 201 across the 54 of their papers we have counts for
57 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…
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…
Distributive laws between the operads Lie and Com
Murray Bremner, Vladimir Dotsenko
Using methods of computer algebra, especially Gröbner bases for submodules of free modules over polynomial rings, we solve a classification problem in theory of algebraic operads:…
Enumeration and Asymptotic Formulas for Rectangular Partitions of the Hypercube
Yu Hin Au, Fatemeh Bagherzadeh, Murray R. Bremner
We study a two-parameter generalization of the Catalan numbers: is the number of ways to subdivide the -dimensional hypercube into rectangular blocks using orth…
Operadic approach to cohomology of associative triple and N-tuple systems
Fatemeh Bagherzadeh, Murray Bremner
The cup product in the cohomology of algebras over quadratic operads has been studied in the general setting of Koszul duality for operads. We study the cup product on the cohomolo…