Vol. 3, No. 8, 2009

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

Volume 18
Issue 4, 631–846
Issue 3, 409–629
Issue 2, 209–408
Issue 1, 1–208

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

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
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
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