The Elliptic Drinfeld Center of a Premodular Category
Quantum Algebra
2020-12-04 v2
Abstract
Given a tensor category C, one constructs its Drinfeld center Z(C) which is a braided tensor category, having as objects pairs (X, lambda), where X in Obj(C) and lambda is a half-braiding. For a premodular category C, we construct a new category Zel(C) which we call the Elliptic Drinfeld Center, which has objects (X, lambda1, lambda2), where the lambda i's are half-braidings that satisfy some compatibility conditions. We discuss an SL2(Z)-action on Zel(C) that is related to the anomaly appearing in Reshetikhin-Turaev theory. This construction is motivated from the study of the extended Crane-Yetter TQFT, in particular the category associated to the once punctured torus.
Keywords
Cite
@article{arxiv.1904.09511,
title = {The Elliptic Drinfeld Center of a Premodular Category},
author = {Ying Hong Tham},
journal= {arXiv preprint arXiv:1904.09511},
year = {2020}
}
Comments
Fixed error in proof of semisimplicity of Z(C) and Zel(C)