Deformations of skew group algebras of symmetric groups

05/01/2018 - 12:15pm
05/01/2018 - 1:10pm
Briana Foster-Greenwood (Cal Poly Pomona)

Many noncommutative algebras arise as deformations of commutative algebras. For instance, the Weyl algebra is a deformation of the polynomial ring R[x,y] obtained by replacing the commutative relation yx-xy=0 with the noncommutative relation yx-xy=1. For a twist, we consider skew group algebras formed as the semi-direct product of a polynomial algebra and a group algebra. Gradings, filtrations, and degrees play an important role in the deformation theory of skew group algebras. Graded Hecke algebras (including symplectic reflection algebras and rational Cherednik algebras), for instance, are deformations in which commutators of vectors of degree 1 are set to elements of the group algebra, which have degree 0. Work of Shepler and Witherspoon extends the theory to deformations where commutators of vectors of degree 1 are set to combinations of elements of degrees 1 and 0. In this talk we use invariant theory and cohomology to explore such deformations for skew group algebras arising from single and doubled permutation representations of the symmetric group. Joint work with Cathy Kriloff (Idaho State University).

Millikan 2099, Pomona College

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