Group cohomology and gauge equivalence of some twisted quantum doubles
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- by Geoffrey Mason and Siu-Hung Ng PDF
- Trans. Amer. Math. Soc. 353 (2001), 3465-3509 Request permission
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.References
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Additional Information
- Geoffrey Mason
- Affiliation: Department of Mathematics, University of California, Santa Cruz, California 95064
- MR Author ID: 189334
- 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
- MR Author ID: 343929
- Email: rng@towson.edu
- 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.
- © Copyright 2001 American Mathematical Society
- 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
- MathSciNet review: 1837244