The Hochschild cohomology ring of a global quotient orbifold

The Hochschild Cohomology Ring modulo Nilpotence of a Monomial Algebra

For a finite dimensional monomial algebra Λ over a field K we show that the Hochschild cohomology ring of Λ modulo the ideal generated by homogeneous nilpotent elements is a commutative finitely generated Kalgebra of Krull dimension at most one. This was conjectured to be true for any finite dimensional algebra over a field in [13].

Orbifold Cup Products and Ring Structures on Hochschild Cohomologies

In this paper we study the Hochschild cohomology ring of convolution algebras associated to orbifolds, as well as their deformation quantizations. In the first case the ring structure is given in terms of a wedge product on twisted polyvectorfields on the inertia orbifold. After deformation quantization, the ring structure defines a product on the cohomology of the inertia orbifold. We study th...

The Orbifold Cohomology Ring of Simplicial Toric Stack Bundles

We compute the orbifold cohomology ring of the simplicial toric stack bundles. We give an example to show that the ordinary cohomology ring of the crepant resolution of a simplicial toric stack bundle is not necessarily isomorphic to its orbifold cohomology ring.

Orbifold Cohomology of a Wreath Product Orbifold

Abstract. Let [X/G] be an orbifold which is a global quotient of a compact almost complex manifold X by a finite group G. Let Σn be the symmetric group on n letters. Their semidirect product G ⋊ Σn is called the wreath product of G and it naturally acts on the n-fold product X, yielding the orbifold [X/(G ⋊Σn)]. Let H (X , G ⋊Σn) be the stringy cohomology [FG, JKK1] of the (G ⋊ Σn)-space X . Wh...

Second Hochschild Cohomology of Convolution Algebras