1998/08/31 by D. Nikshych, L. Vainerman
Mathematics · #math.QA #math.OA
published as Lecture Notes in Pure and Appl. Math, 209 (2000), 189-221 · Latex, 38 pages, minor errors corrected
arxiv created 1998/11/04 · arxiv updated 2009/11/30
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.