Contact｜Sitemap｜HOME｜Japanese
HOME > Table of Contents and Abstracts > Vol. 68, No. 3
Tohoku Mathematical Journal
2016
September
SECOND SERIES VOL. 68, NO. 3
Tohoku Math. J.
68 (2016), 377405

Title
CROSSED ACTIONS OF MATCHED PAIRS OF GROUPS ON TENSOR CATEGORIES
Author
Sonia Natale
(Received June 9, 2014, revised October 29, 2014) 
Abstract.
We introduce the notion of $(G, \Gamma)$crossed action on a tensor category, where $(G, \Gamma)$ is a matched pair of finite groups. A tensor category is called a $(G, \Gamma)$crossed tensor category if it is endowed with a $(G, \Gamma)$crossed action. We show that every $(G,\Gamma)$crossed tensor category $\mathcal{C}$ gives rise to a tensor category $\mathcal{C}^{(G, \Gamma)}$ that fits into an exact sequence of tensor categories $\operatorname{Rep} G \toto \mathcal{C}^{(G, \Gamma)} \toto \mathcal{C}$. We also define the notion of a $(G, \Gamma)$braiding in a $(G, \Gamma)$crossed tensor category, which is connected with certain settheoretical solutions of the QYBE. This extends the notion of $G$crossed braided tensor category due to Turaev. We show that if $\mathcal{C}$ is a $(G, \Gamma)$crossed tensor category equipped with a $(G, \Gamma)$braiding, then the tensor category $\mathcal{C}^{(G, \Gamma)}$ is a braided tensor category in a canonical way.
Mathematics Subject Classification.
Primary 18D10; Secondary 16T05.
Key words and phrases.
Tensor category, exact sequence, matched pair, crossed action, braided tensor category, crossed braiding.


To the top of this page
Back to the Contents