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The relative monoidal center and tensor products of monoidal categories.
- Source :
- Communications in Contemporary Mathematics; Dec2020, Vol. 22 Issue 8, pN.PAG-N.PAG, 53p
- Publication Year :
- 2020
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- TENSOR products
QUANTUM groups
HOPF algebras
CATEGORIES (Mathematics)
Subjects
Details
- Language :
- English
- ISSN :
- 02191997
- Volume :
- 22
- Issue :
- 8
- Database :
- Complementary Index
- Journal :
- Communications in Contemporary Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 145385080
- Full Text :
- https://doi.org/10.1142/S0219199719500688