Wakui, Michihisa Triangular structures of Hopf algebras and tensor Morita equivalences. (English) Zbl 1218.16022 Rev. Unión Mat. Argent. 51, No. 1, 193-210 (2010). 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. Cited in 3 Documents 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 Keywords:triangular structures; Hopf algebras; tensor Morita invariants; monoidally equivalent module categories Citations:Zbl 1215.16021 PDFBibTeX XMLCite \textit{M. Wakui}, Rev. Unión Mat. Argent. 51, No. 1, 193--210 (2010; Zbl 1218.16022)