The First Hochschild Cohomology Group of a Cluster tilted Algebra Revisited

The first Hochschild cohomology group of a schurian cluster-tilted algebra

Given a cluster-tilted algebra B we study its first Hochschild cohomology group HH(B) with coefficients in the B-B-bimodule B. We find several consequences when B is representation-finite, and also in the case where B is cluster-tilted of type Ã. 2000 Mathematics Subject Classification : 16E40

Second Hochschild Cohomology of Convolution Algebras

Galois coverings of weakly shod algebras

We investigate the Galois coverings of weakly shod algebras. For a weakly shod algebra not quasi-tilted of canonical type, we establish a correspondence between its Galois coverings and the Galois coverings of its connecting component. As a consequence we show that a weakly shod algebra which is not quasi-tilted of canonical type is simply connected if and only if its first Hochschild cohomolog...

The Lie Module Structure on the Hochschild Cohomology Groups of Monomial Algebras with Radical Square Zero

We study the Lie module structure given by the Gerstenhaber bracket on the Hochschild cohomology groups of a monomial algebra with radical square zero. The description of such Lie module structure will be given in terms of the combinatorics of the quiver. The Lie module structure will be related to the classification of finite dimensional modules over simple Lie algebras when the quiver is give...

On the Hochschild Cohomology of Tame Hecke Algebras

In this paper we are interested in Hochschild cohomology of finite-dimensional algebras; the main motivation is to generalize group cohomology to larger classes of algebras. If suitable finite generation holds, one can define support varieties of modules as introduced by [SS]. Furthermore, when the algebra is self-injective, many of the properties of group representations generalize to this set...