Related papers: Derivation over twisted group ring and its applica…

We formulate the Gerstenhaber algebra structure of Hochschild cohomology of finite group extensions of some quantum complete intersections. When the group is trivial, this work characterizes the graded Lie brackets on Hochschild cohomology…

The Temperley-Lieb and Brauer algebras and their cyclotomic analogues, as well as the partition algebra, are all examples of twisted semigroup algebras. We prove a general theorem about the cellularity of twisted semigroup algebras of…

We compute the Hochschild cohomology groups of the cluster-tilted algebras of finite representation type.

This article is devoted to the investigation of the deformation (twisting) of monoidal structures, such as the associativity constraint of the monoidal category and the monoidal structure of monoidal functor. The sets of twistings have a…

We classify the derivations of degree-one generalized Weyl algebras over a univariate Laurent polynomial ring. In particular, our results cover the Weyl-Hayashi algebra, a quantization of the first Weyl algebra arising as a primitive factor…

Any cluster-tilted algebra is the relation extension of a tilted algebra. We present a method to, given the distribution of a cluster-tilting object in the Auslander-Reiten quiver of the cluster category, construct all tilted algebras whose…

We describe the fine (group) gradings on the Heisenberg algebras, on the Heisenberg superalgebras and on the twisted Heisenberg algebras. We compute the Weyl groups of these gradings. Also the results obtained respect to Heisenberg…

In this note, our goal is to describe the concept of generalized derivations in the context of BiHom-supertrialgebras. We provide a comprehensive analysis of the properties and applications of these generalized derivations, including their…

Let k be any field. We consider the Hopf-Schur group of k, defined as the subgroup of the Brauer group of k consisting of classes that may be represented by homomorphic images of Hopf algebras over k. We show here that twisted group…

In this paper we investigate left ideals as codes in twisted skew group rings. The considered rings, which are often algebras over a finite field, allows us to detect many of the well-known codes. The presentation, given here, unifies the…

We define several versions of the cohomology ring of an associative algebra. These ring structures unify some well known operations from homological algebra and differential geometry. They have some formal resemblance with the quantum…

In this note we study a family of algebras with one parameter defined by generators and relations. The set of generators contains the generators of the usual braids algebra, and another set of generators which is interpreted as ties between…

We determine explicitly the center of the twisted graded Hecke algebras associated to homocyclic groups. Our results are a generalization of formulas by M. Douglas and B. Fiol in [J. High Energy Phys. 2005 (2005), no. 9, 053, 22 pages,…

This work adapts the equivalent definitions of division algebras over a field into multiple types of division algebras in a monoidal category. Examples and consequences of these definitions are then established in various monoidal settings.

This is a further investigation of our approach to group actions in homological algebra in the settings of homology of {\Gamma}-simplicial groups, particularly of {\Gamma}-equivariant homology and cohomology of {\Gamma}-groups. This…

This paper is centered around the classical problem of extracting properties of a finite group $G$ from the ring isomorphism class of its integral group ring $\mathbb{Z} G$. This problem is considered via describing the unit group…

We describe the Hochschild cohomology ring for a family of self-injective algebras of tree class $E_6$ in terms of generators and relations. Together with the results of the previous paper, this gives a complete description of the…

Leo Creedon and Kieran Hughes in [18] studied derivations of a group ring $RG$ (of a group $G$ over a commutative unital ring $R$) in terms of generators and relators of group $G$. In this article, we do that for $(\sigma,…

We consider associative algebras L over a field provided with a direct sum decomposition of a two-sided ideal M and a sub-algebra A - examples are provided by trivial extensions or triangular type matrix algebras. In this relative and split…

This article is an expository account of the theory of twisted commutative algebras, which simply put, can be thought of as a theory for handling commutative algebras with large groups of linear symmetries. Examples include the coordinate…