Preantipodes for dual-quasi bialgebras

Details Preantipodes for dual-quasi bialgebras Preantipodes for dual-quasi bialgebras

2010-12-09

arxiv.org/abs/1012.1956v1

Mathematics

Quantum Algebra

Scientific paper

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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