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Yetter-Drinfeld modules over weak multiplier bialgebras

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Abstract

We continue the study of the representation theory of a regular weak multiplier bialgebra with full comultiplication, started in [4, 2]. Yetter-Drinfeld modules are defined as modules and comodules, with compatibility conditions that are equivalent to a canonical object being (weakly) central in the category of modules, and equivalent also to another canonical object being (weakly) central in the category of comodules. Yetter-Drinfeld modules are shown to constitute a monoidal category via the (co)module tensor product over the base (co)algebra. Finite-dimensional Yetter-Drinfeld modules over a regular weak multiplier Hopf algebra with full comultiplication are shown to possess duals in this monoidal category.

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Authors and Affiliations

  1. Wigner Research Centre for Physics, H-1525, Budapest 114, P.O.B. 49, Hungary

    Gabriella Böhm

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  1. Gabriella Böhm
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Correspondence to Gabriella Böhm.

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This research was supported by the Hungarian Scientific Research Fund OTKA, grant K108384.

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Böhm, G. Yetter-Drinfeld modules over weak multiplier bialgebras. Isr. J. Math. 209, 85–123 (2015). https://doi.org/10.1007/s11856-015-1212-6

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  • DOI: https://doi.org/10.1007/s11856-015-1212-6

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