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- W3206449577 abstract "AbstractAbstractWe prove a number of structural and representation-theoretic results on linearly reductive quantum groups, i.e., objects dual to those of cosemisimple Hopf algebras: (a) a closed normal quantum subgroup is automatically linearly reductive if its squared antipode leaves invariant each simple subcoalgebra of the underlying Hopf algebra; (b) for a normal embedding H⊴G there is a Clifford-style correspondence between two equivalence relations on irreducible G- and, respectively, H-representations; and (c) given an embedding H≤G of linearly reductive quantum groups, the Pontryagin dual of the relative center Z(G)∩H can be described by generators and relations, with one generator gV for each irreducible G-representation V and one relation gU=gVgW whenever U and V⊗W are not disjoint over H.This latter center-reconstruction result generalizes and recovers Müger’s compact-group analogue and the author’s quantum-group version of that earlier result by setting H=G.Keywords: Antipodecentercomodulecosemisimple Hopf algebracotensorlinearly reductiveQuantum group2020 Mathematics Subject Classification: 16T0520G4216T20 AcknowledgmentsI am also very grateful for the anonymous referee’s comments on an earlier version of the paper.Additional informationFundingThis work is partially supported by NSF grant DMS-2001128." @default.
- W3206449577 created "2021-10-25" @default.
- W3206449577 creator A5076253324 @default.
- W3206449577 date "2023-03-11" @default.
- W3206449577 modified "2023-10-14" @default.
- W3206449577 title "Normal subgroups and relative centers of linearly reductive quantum groups" @default.
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- W3206449577 doi "https://doi.org/10.1080/00927872.2023.2186702" @default.
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