Zobrazeno 1 - 10
of 248
pro vyhledávání: '"BREMNER, MURRAY"'
Autor:
Bremner, Murray, Dotsenko, Vladimir
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 classification problem: we find all Koszul operads among those encoding associ
Externí odkaz:
http://arxiv.org/abs/2203.11142
Autor:
Bremner, Murray R., Elgendy, Hader A.
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 algebra applied to determinantal ideals of matrices over polynomial rings.
Externí odkaz:
http://arxiv.org/abs/2109.04391
Autor:
Bremner, Murray, Dotsenko, Vladimir
Using methods of computer algebra, especially Gr\"obner bases for submodules of free modules over polynomial rings, we solve a classification problem in theory of algebraic operads: we show that the only nontrivial (possibly inhomogeneous) distributi
Externí odkaz:
http://arxiv.org/abs/1912.05519
Publikováno v:
Journal of Integer Sequences 23 (2020) Article 20.1.4
We study a two-parameter generalization of the Catalan numbers: $C_{d,p}(n)$ is the number of ways to subdivide the $d$-dimensional hypercube into $n$ rectangular blocks using orthogonal partitions of fixed arity $p$. Bremner \& Dotsenko introduced $
Externí odkaz:
http://arxiv.org/abs/1903.00813
We study polynomial identities satisfied by the mutation product $xpy - yqx$ on the underlying vector space of an associative algebra $A$, where $p, q$ are fixed elements of $A$. We simplify known results for identities in degree $4$, proving that on
Externí odkaz:
http://arxiv.org/abs/1812.05481
Autor:
Bagherzadeh, Fatemeh, Bremner, Murray
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 cohomology of n-ary totally associative algebras with an operation of even (ho
Externí odkaz:
http://arxiv.org/abs/1812.03947
Autor:
Bagherzadeh, Fatemeh, Bremner, Murray
Dotsenko and Vallette discovered an extension to nonsymmetric operads of Buchberger's algorithm for Gr\"obner bases of polynomial ideals. In the free nonsymmetric operad with one ternary operation $({\ast}{\ast}{\ast})$, we compute a Gr\"obner basis
Externí odkaz:
http://arxiv.org/abs/1810.04042
Autor:
Bremner, Murray, Markl, Martin
By the Three Graces we refer, following J.-L. Loday, to the algebraic operads Ass, Com, and Lie, each generated by a single binary operation; algebras over these operads are respectively associative, commutative associative, and Lie. We classify all
Externí odkaz:
http://arxiv.org/abs/1809.08191