Braided Drinfeld and Heisenberg doubles

• Robert Laugwitz ^[1]
  1. [1] University of Oxford

     University of Oxford

     Oxford District, Reino Unido

     
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 10 (October 2015), 2015, págs. 4541-4596
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2015.02.031
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• Resumen

  • 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.