Hochschild cohomology of some quantum complete intersections

Hochschild Cohomology and Quantum Drinfeld Hecke Algebras

Abstract. Quantum Drinfeld Hecke algebras are generalizations of Drinfeld Hecke algebras in which polynomial rings are replaced by quantum polynomial rings. We identify these algebras as deformations of skew group algebras, giving an explicit connection to Hochschild cohomology. We compute the relevant part of Hochschild cohomology for actions of many reflection groups and we exploit computatio...

Second Hochschild Cohomology of Convolution Algebras

On some Hochschild cohomology classes of fusion algebras

The obstructions for an arbitrary fusion algebra to be a fusion algebra of some semisimple monoidal category are constructed. Those obstructions lie in groups which are closely related to the Hochschild cohomology of fusion algebras with coefficients in the K-theory of the ground (algebraically closed) field. The special attention is devoted to the case of fusion algebra of invariants of finite...

Quantum random walks and vanishing of the second Hochschild cohomology

Given a conditionally completely positive map L on a unital ∗-algebra A, we find an interesting connection between the second Hochschild cohomology of A with coefficients in the bimodule EL = Ba(A⊕M) of adjointable maps, where M is the GNS bimodule of L, and the possibility of constructing a quantum random walk (in the sense of [2, 11, 13, 16]) corresponding to L.

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...