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Integral theory for Hopf Algebroids

Gabriella Böhm
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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.

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BibTeXRIS

Gabriella Böhm. 2008-12-09. Integral theory for Hopf Algebroids. https://arxiv.org/abs/math/0403195

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