Hochschild cohomology of some quantum complete intersections

Abstract

We compute the Hochschild cohomology ring of the algebras $A=k⟨X,Y⟩/(X^a,XY-qYX,Y^a)$ over a field $k$ where $a\ge 2$ and where $q\in k$ is a primitive $a$-th root of unity. We find the the dimension of ${\mathrm{HH}}^n(A)$ and show that it is independent of $a$. We compute explicitly the ring structure of the even part of the Hochschild cohomology modulo homogeneous nilpotent elements.

16 pages

References in corpus (2)

• Support varieties for selfinjective algebras
• The Hochschild cohomology ring of a Frobenius algebra with semisimple Nakayama automorphism is a Batalin-Vilkovisky algebra

Cited by in corpus (2)

• Maximal tori in $H{H}^1$ and the fundamental group
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