Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Twisted Quantum Doubles and the McKay Correspondence   We consider a class of quasi-Hopf algebras which we call \emph{generalized
twisted quantum doubles}. They are abelian extensions $H = \mb{C}[\bar{G}]
\bowtie \mb{C}[G]$ ($G$ is a finite group and $\bar{G}$ a homomorphic image),
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 $SU_2(\mb{C})$ then $H$ exhibits an orbifold McKay
Correspondence: certain fusion rules of $H$ define a graph with connected
components indexed by conjugacy classes of $\bar{G}$, 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 $\bar{G} = 1$.

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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: hep-th