Algebraic Versions of a Finite-Dimensional Quantum Groupoid

Details Algebraic Versions of a Finite-Dimensional Quantum Groupoid Algebraic Versions of a Finite-Dimensional Quantum Groupoid

1998-08-12

arxiv.org/abs/math/9808054v2

Lecture Notes in Pure and Appl. Math, 209 (2000), 189-221

Mathematics

Quantum Algebra

Latex, 38 pages, minor errors corrected

Scientific paper

We establish the equivalence of three versions of a finite dimensional quantum groupoid: a generalized Kac algebra introduced by T. Yamanouchi, a weak $C^*$-Hopf algebra introduced by G. Bohm, F. Nill and K. Szlachanyi (with an involutive antipode), and a Kac bimodule -- an algebraic version of a Hopf bimodule, the notion introduced by J.-M. Vallin. We also study the structure and construct examples of finite dimensional quantum groupoids.

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