Preantipodes for dual-quasi bialgebras

2010/12/09 by Alessandro Ardizzoni, Ardizzoni, Alessandro, Alice Pavarin +1 · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1012.1956

Abstract

It is known that a dual quasi-bialgebra with antipode H, i.e. a dual quasi-Hopf algebra, fulfils a fundamental theorem for right dual quasi-Hopf H-bicomodules. The converse in general is not true. We prove that, for a dual quasi-bialgebra H, the structure theorem amounts to the existence of a suitable map S:H→ H that we call a preantipode of H.

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• Reflection of Nichols Algebras over Coquasi-Hopf Algebras
• Equivariant Eilenberg-Watts theorem for module coalgebras

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