The relative monoidal center and tensor products of monoidal categories

Laugwitz, Robert (2020) The relative monoidal center and tensor products of monoidal categories. Communications in Contemporary Mathematics, 22 (8). ISSN 0219-1997

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This paper develops a theory of monoidal categories relative to a braided monoidal category, called augmented monoidal categories. For such categories, balanced bimodules are defined using the formalism of balanced functors. It is shown that there exists a monoidal structure on the relative tensor product of two augmented monoidal categories which is Morita dual to a relative version of the monoidal center. In examples, a category of locally finite weight modules over a quantized enveloping algebra is equivalent to the relative monoidal center of modules over its Borel part. A similar result holds for small quantum groups, without restricting to locally finite weight modules. More generally, for modules over bialgebras inside a braided monoidal category, the relative center is shown to be equivalent to the category of Yetter-Drinfeld modules inside the braided category. If the braided category is given by modules over a quasitriangular Hopf algebra, then the relative center corresponds to modules over a braided version of the Drinfeld double (i.e. the double bosonization in the sense of Majid) which are locally finite for the action of the dual.

Item Type: Article
Uncontrolled Keywords: braided monoidal categories,categorical modules,monoidal center,relative tensor product,mathematics(all),applied mathematics ,/dk/atira/pure/subjectarea/asjc/2600
Faculty \ School: Faculty of Science > School of Mathematics
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Depositing User: LivePure Connector
Date Deposited: 04 Oct 2019 11:30
Last Modified: 22 Oct 2022 05:18
DOI: 10.1142/S0219199719500688

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