English

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 CC^*-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

R2 v1 2026-07-22T17:59:36.663Z