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arXiv · 1904.09511

The Elliptic Drinfeld Center of a Premodular Category

Ying Hong Tham
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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.

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BibTeXRIS

Ying Hong Tham. 2019-04-20. The Elliptic Drinfeld Center of a Premodular Category. https://arxiv.org/abs/1904.09511

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