Crossed Interval Groups and Operations on the Hochschild Cohomology

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...

Second Hochschild Cohomology of Convolution Algebras

Products in Hochschild Cohomology and Grothendieck Rings of Group Crossed Products

We give a general construction of rings graded by the conjugacy classes of a finite group. Some examples of our construction are the Hochschild cohomology ring of a finite group algebra, the Grothendieck ring of the Drinfel’d double of a group, and the orbifold cohomology ring for a global quotient. We generalize the first two examples by deriving product formulas for the Hochschild cohomology ...

Green functors, crossed G-monoids, and Hochschild constructions

Let G be a finite group, and R be a commutative ring. This note proposes a generalization to any Green functor for G over R of the construction of the Hochschild cohomology ring HH∗(G,R) from the ordinary cohomology functor H∗(−, R). Another special case is the construction of the crossed Burnside ring of G from the ordinary Burnside functor. The general abstract setting is the following : let ...

Dyer-Lashof-Cohen operations in Hochschild cohomology

In the paper we give explicit formulae for operations in Hochschild cohomology which are analogous to the operations in the homology of double loop spaces. As a corollary we obtain that any brace algebra in finite characteristics is always a restricted Lie algebra.