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Integral Theory for Hopf Algebroids

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An Erratum to this article was published on 04 December 2009

Abstract

The theory of integrals is used to analyze the structure of Hopf algebroids. We prove that the total algebra of a 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. It is a Frobenius extension if and only if the Hopf algebroid possesses a nondegenerate 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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Authors and Affiliations

  1. Research Institute for Particle and Nuclear Physics, H-1525, Budapest 114, POB 49, Hungary

    Gabriella Böhm

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  1. Gabriella Böhm
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Correspondence to Gabriella Böhm.

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Mathematics Subject Classification (2000)

16W30.

An erratum to this article is available at http://dx.doi.org/10.1007/s10468-009-9167-0.

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Böhm, G. Integral Theory for Hopf Algebroids. Algebr Represent Theor 8, 563–599 (2005). https://doi.org/10.1007/s10468-005-8760-0

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