Deformation of finite dimensional C*-quantum groupoids

Details Deformation of finite dimensional C*-quantum groupoids Deformation of finite dimensional C*-quantum groupoids

2003-10-17

arxiv.org/abs/math/0310265v1

Mathematics

Quantum Algebra

Scientific paper

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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