The twisted Drinfeld double of a finite group via gerbes and finite groupoids

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 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.

PDF Access Denied

Warning: We have not been able to recognize your IP address 47.88.87.18 as that of a subscriber to this journal. Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form.

Or, visit our subscription page for instructions on purchasing a subscription. You may also contact us at contact@msp.org or by using our contact form.

Or, you may purchase this single article for USD 29.95:

Keywords

Dijkgraaf–Witten theory, quantum double, transgression

Mathematical Subject Classification 2000

Primary: 57R56

Secondary: 16W30, 18B40

References

Publication

Received: 19 December 2006

Accepted: 10 July 2008

Published: 3 September 2008

Authors

Simon Willerton
Department of Pure Mathematics University of Sheffield Hicks Building Hounsfield Road Sheffield, S3 7RH UK

Volume 8, issue 3 (2008)

Simon Willerton

Abstract