Hochschild Cohomology of Truncated Polynomials

Poisson (co)homology of truncated polynomial algebras in two variables

We study the Poisson (co)homology of the algebra of truncated polynomials in two variables viewed as the semi-classical limit of a quantum complete intersection studied by Bergh and Erdmann. We show in particular that the Poisson cohomology ring of such a Poisson algebra is isomorphic to the Hochschild cohomology ring of the corresponding quantum complete intersection.

Second Hochschild Cohomology of Convolution Algebras

2 00 5 Hochschild cohomology of truncated quiver algebras ∗

For a truncated quiver algebra over a field of arbitrary characteristic, its Hochschild cohomology is calculated. Moreover, it is shown that its Hochschild cohomology algebra is finitedimensional if and only if its global dimension is finite if and only if its quiver has no oriented cycles. MSC(2000): 16E40, 16E10, 16G10

Comparison Morphisms and the Hochschild Cohomology Ring of Truncated Quiver Algebras

A main contribution of this paper is the explicit construction of comparison morphisms between the standard bar resolution and Bardzell’s minimal resolution for truncated quiver algebras (TQA’s). As a direct application we describe explicitely the Yoneda product and derive several results on the structure of the cohomology ring of TQA’s. For instance, we show that the product of odd degree coho...

Finite Groups Acting Linearly: Hochschild Cohomology and the Cup Product

When a finite group acts linearly on a complex vector space, the natural semi-direct product of the group and the polynomial ring over the space forms a skew group algebra. This algebra plays the role of the coordinate ring of the resulting orbifold and serves as a substitute for the ring of invariant polynomials from the viewpoint of geometry and physics. Its Hochschild cohomology predicts var...