arXiv subjects

Sarah J. Witherspoon

Publications and source records attributed to Sarah J. Witherspoon.

5 recordsLinked to original sources

arXiv2011

Drinfeld Orbifold Algebras

We define Drinfeld orbifold algebras as filtered algebras deforming the skew group algebra (semi-direct product) arising from the action of a finite group on a polynomial ring. They simultaneously generalize Weyl algebras, graded (or Drinfeld) Hecke algebras, rational Cherednik algebras, symplectic reflection algebras, and universal enveloping algebras of Lie algebras with group actions. We give necessary and sufficient conditions on defining parameters to obtain Drinfeld orbifold algebras in two general formats, both algebraic and homological. We explain the connection between Hochschild cohomology and a Poincare-Birkhoff-Witt property explicitly (using Gerstenhaber brackets). We also classify those deformations of skew group algebras which arise as Drinfeld orbifold algebras and give applications for abelian groups.

math.RA↗

arXiv2006

Skew Derivations and Deformations of a Family of Group Crossed Products

We obtain deformations of a crossed product of a polynomial algebra with a group, under some conditions, from universal deformation formulas. We show that the resulting deformations are nontrivial by a comparison with Hochschild cohomology. The universal deformation formulas arise from actions of Hopf algebras generated by automorphisms and skew derivations, and are universal in the sense that they apply to deform all algebras with such Hopf algebra actions.

math.RA↗

arXiv2005

Twisted Graded Hecke Algebras

We generalize graded Hecke algebras to include a twisting two-cocycle for the associated finite group. We give examples where the parameter spaces of the resulting twisted graded Hecke algebras are larger than that of the graded Hecke algebras. We prove that twisted graded Hecke algebras are particular types of deformations of a crossed product.

math.RT↗

arXiv2002

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 ring of a group crossed product and for the Grothendieck ring of an abelian extension of Hopf algebras. Our results account for similarities in the product structures among these examples.

math.RA↗

arXiv2001

Clifford correspondence for algebras

We give a Clifford correspondence for an algebra A over an algebraically closed field, that is an algorithm for constructing some finite-dimensional simple A-modules from simple modules for a subalgebra and endomorphism algebras. This applies to all finite-dimensional simple A-modules in the case that A is finite-dimensional and semisimple with a given semisimple subalgebra. We discuss connections between our work and earlier results, with a view towards applications particularly to finite-dimensional semisimple Hopf algebras.

math.RA↗