Integral theory for Hopf Algebroids
Abstract
The theory of integrals is used to analyse the structure of Hopf algebroids, introduced in math.QA/0302325. We prove that the total algebra of the Hopf algebroid is a separable extension of the base algebra if and only if it is a semi-simple extension and if and only if the Hopf algebroid possesses a normalized integral. The total algebra of a finitely generated and projective Hopf algebroid is a Frobenius extension of the base algebrahe Hopf algebroid possesses anormalized integral. We give also a sufficient and necessary condition in terms of integrals under which it is a quasi-Frobenius extension and illustrate by an example that this condition does not hold true in general. Our results are generalizations of classical results on Hopf algebras.
Cite
@article{arxiv.math/0403195,
title = {Integral theory for Hopf Algebroids},
author = {Gabriella Böhm},
journal= {arXiv preprint arXiv:math/0403195},
year = {2008}
}
Comments
LaTeX2e file 30 pages, no figures. v4:missing assumptions added in Thms 4.2, 4.7 and 5.2, new Corollary 4.8