Braided Drinfeld and Heisenberg doubles

Laugwitz, Robert

Abstract

© 2015 Elsevier B.V. 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 of Lu [22] that the Heisenberg double is a 2-cocycle twist of the Drinfeld double for general braided Hopf algebras.

• Journal Article Type: Article
• Acceptance Date: Feb 11, 2015
• Online Publication Date: Mar 13, 2015
• Publication Date: 2015-10
• Deposit Date: Nov 28, 2019
• Publicly Available Date: Jan 20, 2020
• Journal: Journal of Pure and Applied Algebra
• Print ISSN: 0022-4049
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 219
• Issue: 10
• Pages: 4541-4596
• DOI: https://doi.org/10.1016/j.jpaa.2015.02.031
• Public URL: https://nottingham-repository.worktribe.com/output/3440562
• Additional Information: This article is maintained by: Elsevier; Article Title: Braided Drinfeld and Heisenberg doubles; Journal Title: Journal of Pure and Applied Algebra; CrossRef DOI link to publisher maintained version: https://doi.org/10.1016/j.jpaa.2015.02.031; Content Type: article; Copyright: Copyright © 2015 Elsevier B.V. All rights reserved.