Algebraic Versions of a Finite-Dimensional Quantum Groupoid
Quantum Algebra
2007-05-23 v2 Operator Algebras
Abstract
We establish the equivalence of three versions of a finite dimensional quantum groupoid: a generalized Kac algebra introduced by T. Yamanouchi, a weak -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.
Keywords
Cite
@article{arxiv.math/9808054,
title = {Algebraic Versions of a Finite-Dimensional Quantum Groupoid},
author = {D. Nikshych and L. Vainerman},
journal= {arXiv preprint arXiv:math/9808054},
year = {2007}
}
Comments
Latex, 38 pages, minor errors corrected