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.
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
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
