The twisted Drinfeld double of a finite group via gerbes and finite groupoids
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Publication:945666
DOI10.2140/AGT.2008.8.1419zbMATH Open1154.57029arXivmath/0503266OpenAlexW3098501141MaRDI QIDQ945666
Author name not available (Why is that?)
Publication date: 17 September 2008
Published in: (Search for Journal in Brave)
Abstract: The twisted Drinfeld double (or quasi-quantum double) of a finite group with a 3-cocycle is identified with a certain twisted groupoid algebra. The groupoid is the loop (or inertia) groupoid of the original group and the twisting is shown geometrically to be the loop transgression of the 3-cocycle. The twisted representation theory of finite groupoids is developed and used to derive properties of the Drinfeld double, such as representations being classified by their characters. This is all motivated by gerbes and 3-dimensional topological quantum field theory. In particular the representation category of the twisted Drinfeld double is viewed as the `space of sections' associated to a transgressed gerbe over the loop groupoid.
Full work available at URL: https://arxiv.org/abs/math/0503266
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