Vol. 3, No. 8, 2009

Download this article
Download this article For screen
For printing
Recent Issues

Volume 11, 1 issue

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
Cover
Editorial Board
Editors' Addresses
Editors' Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Centers of graded fusion categories

Shlomo Gelaki, Deepak Naidu and Dmitri Nikshych

Vol. 3 (2009), No. 8, 959–990
Abstract

Let C be a fusion category faithfully graded by a finite group G and let D be the trivial component of this grading. The center Z(C) of C is shown to be canonically equivalent to a G-equivariantization of the relative center ZD(C). We use this result to obtain a criterion for C to be group-theoretical and apply it to Tambara–Yamagami fusion categories. We also find several new series of modular categories by analyzing the centers of Tambara–Yamagami categories. Finally, we prove a general result about the existence of zeroes in S-matrices of weakly integral modular categories.

Keywords
fusion categories, braided categories, graded tensor categories
Mathematical Subject Classification 2000
Primary: 16W30
Secondary: 18D10
Milestones
Received: 21 May 2009
Revised: 31 August 2009
Accepted: 9 November 2009
Published: 25 December 2009
Authors
Shlomo Gelaki
Department of Mathematics
Technion-Israel Institute of Technology
32000 Haifa
Israel
Deepak Naidu
Department of Mathematics
Texas A&M University
College Station, TX 77843
United States
Dmitri Nikshych
Department of Mathematics and Statistics
University of New Hampshire
Durham, NH 03824
United States