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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Group cohomology and gauge equivalence of some twisted quantum doubles


Authors: Geoffrey Mason and Siu-Hung Ng
Journal: Trans. Amer. Math. Soc. 353 (2001), 3465-3509
MSC (2000): Primary 57T05, 16S40, 16W30
DOI: https://doi.org/10.1090/S0002-9947-01-02771-4
Published electronically: April 24, 2001
MathSciNet review: 1837244
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Abstract: We study the module category associated to the quantum double of a finite abelian group $G$ twisted by a 3-cocycle, which is known to be a braided monoidal category, and investigate the question of when two such categories are equivalent. We base our discussion on an exact sequence which interweaves the ordinary and Eilenberg-Mac Lane cohomology of $G$. Roughly speaking, this reveals that the data provided by such module categories is equivalent to (among other things) a finite quadratic space equipped with a metabolizer, and also a pair of rational lattices $L\subseteq M$ with $L$ self-dual and integral.


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Additional Information

Geoffrey Mason
Affiliation: Department of Mathematics, University of California, Santa Cruz, California 95064
Email: gem@cats.ucsc.edu

Siu-Hung Ng
Affiliation: Department of Mathematics, University of California, Santa Cruz, California 95064
Address at time of publication: Department of Mathematics, Towson University, Baltimore, Maryland 21252
Email: rng@towson.edu

DOI: https://doi.org/10.1090/S0002-9947-01-02771-4
Received by editor(s): December 8, 1999
Received by editor(s) in revised form: July 24, 2000
Published electronically: April 24, 2001
Additional Notes: Research of the first author was supported by the National Science Foundation and the Regents of the University of California.
Article copyright: © Copyright 2001 American Mathematical Society