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Triangular structures of Hopf algebras and tensor Morita equivalences. (English) Zbl 1218.16022

Summary: The triangular structures of a Hopf algebra \(A\) are discussed as a tensor Morita invariant. It is shown by many examples that triangular structures are useful for detecting whether module categories are monoidally equivalent or not. By counting and comparing the numbers of triangular structures, we give simple proofs of some results obtained in [M. Wakui, J. Pure Appl. Algebra 214, No. 6, 701-728 (2010; Zbl 1215.16021)] without polynomial invariants.

MSC:

16T05 Hopf algebras and their applications
18D10 Monoidal, symmetric monoidal and braided categories (MSC2010)
19A22 Frobenius induction, Burnside and representation rings
16T20 Ring-theoretic aspects of quantum groups

Citations:

Zbl 1215.16021
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