Algebraic deformations arising from orbifolds with discrete torsion

Abstract

We develop methods for computing Hochschild cohomology groups and deformations of crossed product rings. We use these methods to ÿnd deformations of a ring associated to a particular orbifold with discrete torsion, and give a presentation of the center of the resulting deformed ring. This connects with earlier calculations by Vafa and Witten of chiral numbers and deformations of a similar orbifold.

Hochschild cohomology and graded Hecke algebras

“…This proposition appears as part of [5,Thm. 5.4], where it is stated for arbitrary degree and arbitrary resolution P q .…”

“…These potentially different characters χ α g can lead to different semi-invariants. In this broader setting, deformations of S(V )# α G are treated in [5,6,26,27].…”

“…Some small examples of such deformations were given in [5,26]. With these potential deformations in mind, as well as the immediate applications to graded Hecke algebras in this article, we compute the relevant cohomology in two cases:…”

Skew Derivations and Deformations of a Family of Group Crossed Products

“…Such a formula is universal in the sense that it applies to any B-module algebra to yield a formal deformation. Known examples include formulas based on universal enveloping algebras of Lie algebras (see examples and references in [11]) and a formula based on a small noncocommutative bialgebra [4]. In Section 3 we generalize the formula in [4].…”

“…Known examples include formulas based on universal enveloping algebras of Lie algebras (see examples and references in [11]) and a formula based on a small noncocommutative bialgebra [4]. In Section 3 we generalize the formula in [4]. Our universal deformation formula is based on a bialgebra generated by skew-primitive and group-like elements, and depends on a parameter q.…”