The Elliptic Drinfeld Center of a Premodular Category

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.

arXiv commentFixed error in proof of semisimplicity of Z(C) and Zel(C)

References in corpus (4)

• Topological Lattice Models in Four Dimensions
• Integrating quantum groups over surfaces
• Turaev-Viro invariants as an extended TQFT
• String-net model of Turaev-Viro invariants

Cited by in corpus (6)

• Factorization Homology and 4D TQFT
• Reduced Tensor Product on the Drinfeld Center
• The Drinfeld Centre of a Symmetric Fusion Category is 2-Fold Monoidal
• The Symmetric Tensor Product on the Drinfeld Centre of a Symmetric Fusion Category
• On the Category of Boundary Values in the Extended Crane-Yetter TQFT
• Categorical Center of Higher Genera and 4D Factorization Homology