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Deformation of finite dimensional C*-quantum groupoids

Jean-Michel Vallin
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Abstract

In this work we prove, in full details, that any finite dimensional $C^*$-quantum groupoid can be deformed in order that the square of the antipode is the identity on the base. We also prove that for any $C^*$-quantum groupoid with non abelian base, there is uncountably many $C^*$-quantum groupoids with the same underlying algebra structure but which are not isomorphic to it. In fact, the $C^*$-quantum groupoids are closed in an analog of the procedure presented by D.Nikshych ([N] 3.7) in a more general situation.

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Jean-Michel Vallin. 2003-10-17. Deformation of finite dimensional C*-quantum groupoids. https://arxiv.org/abs/math/0310265

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