Title

Generalized twisted quantum doubles and the McKay correspondence

Authors

Christopher D. Goff, University of the PacificFollow
Geoffrey Mason, University of California, Santa Cruz

Document Type

Article

Publication Title

Journal of Algebra

Department

Mathematics

ISSN

0021-8693

Volume

324

Issue

11

DOI

10.1016/j.jalgebra.2010.07.004

First Page

3007

Last Page

3016

Publication Date

12-1-2010

Abstract

We consider a class of quasiHopf algebras which we call generalized twisted quantum doubles. They are abelian extensions H=C[G¯]∗⋈C[G] (G is a finite group, G¯ a homomorphic image, and * denotes the dual algebra), possibly twisted by a 3-cocycle, and are a natural generalization of the twisted quantum double construction of Dijkgraaf, Pasquier and Roche. We show that if G is a subgroup of SU₂(C) then H exhibits an orbifold McKay Correspondence: certain fusion rules of H define a graph with connected components indexed by conjugacy classes of G¯, each connected component being an extended affine Diagram of type ADE whose McKay correspondent is the subgroup of G stabilizing an element in the conjugacy class. This reduces to the original McKay Correspondence when G¯=1.

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Recommended Citation

Goff, C. D., & Mason, G. (2010). Generalized twisted quantum doubles and the McKay correspondence. Journal of Algebra, 324(11), 3007–3016. DOI: 10.1016/j.jalgebra.2010.07.004
https://scholarlycommons.pacific.edu/cop-facarticles/272