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arXiv · 1012.1956

Preantipodes for dual-quasi bialgebras

Alessandro Ardizzoni·Alice Pavarin
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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 $S:H\rightarrow H$ that we call a preantipode of $H$.

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Alessandro Ardizzoni, Alice Pavarin. 2010-12-09. Preantipodes for dual-quasi bialgebras. https://arxiv.org/abs/1012.1956

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