Braided Drinfeld and Heisenberg Doubles

Abstract

In this paper, the Drinfeld center of a monoidal category is generalized to a class of mixed Drinfeld centers. This gives a unified picture for the Drinfeld center and a natural Heisenberg analogue. Further, there is an action of the former on the latter. This picture is translated to a description in terms of Yetter-Drinfeld and Hopf modules over quasi-bialgebras in a braided monoidal category. Via braided reconstruction theory, intrinsic definitions of braided Drinfeld and Heisenberg doubles are obtained, together with a generalization of the result in [Lu94] that the Heisenberg double is a 2-cocycle twist of the Drinfeld double for general braided Hopf algebras.

76 pages, minor corrections to V2

References in corpus (1)

• Koszulness of Enveloping Algebras Associated to Generalized Yang-Baxter Equations

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• The Relative Monoidal Center and Tensor Products of Monoidal Categories
• Quantum Multiplicative Hypertoric Varieties and Localization
• Comodule Algebras and 2-Cocycles over the (Braided) Drinfeld Double
• Pointed Hopf Algebras with Triangular Decomposition -- A Characterization of Multiparameter Quantum Groups
• Braided commutative algebras over quantized enveloping algebras