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Integral theory for Hopf Algebroids | | Gabriella Böhm
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11 Mar 2004 | | Subject: | Quantum Algebra MSC-class: 16W30 | math.QA | | 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.It is a Frobenius extension if and only if the Hopf algebroid possesses a non-degenerate 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. | | Source: | arXiv, math.QA/0403195 | | Services: | Forum | Review | PDF | Favorites | |
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