Symmetric Hochschild cohomology of twisted group algebras

Hochschild Cohomology of Group Extensions of Quantum Symmetric Algebras

Abstract. Quantum symmetric algebras (or noncommutative polynomial rings) arise in many places in mathematics. In this article we find the multiplicative structure of their Hochschild cohomology when the coefficients are in an arbitrary bimodule algebra. When this bimodule algebra is a finite group extension (under a diagonal action) of a quantum symmetric algebra, we give explicitly the graded...

Second Hochschild Cohomology of Convolution Algebras

Gerstenhaber Brackets on Hochschild Cohomology of Quantum Symmetric Algebras and Their Group Extensions

We construct chain maps between the bar and Koszul resolutions for a quantum symmetric algebra (skew polynomial ring). This construction uses a recursive technique involving explicit formulae for contracting homotopies. We use these chain maps to compute the Gerstenhaber bracket, obtaining a quantum version of the Schouten-Nijenhuis bracket on a symmetric algebra (polynomial ring). We compute b...

Hochschild Cohomology via Incidence Algebras

Given an algebra A we associate an incidence algebra A(Σ) and compare their Hochschild cohomology groups.

Self-injective Algebras and the Second Hochschild Cohomology Group

In this paper we study the second Hochschild cohomology group HH(Λ) of a finite dimensional algebra Λ. In particular, we determine HH(Λ) where Λ is a finite dimensional self-injective algebra of finite representation type over an algebraically closed field K and show that this group is zero for most such Λ; we give a basis for HH(Λ) in the few cases where it is not zero.