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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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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DOI: https://doi.org/10.1007/s10468-005-8760-0