Integral theory for Hopf algebroids

Research output: Contribution to journalArticle

16 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)563-599
Number of pages37
JournalAlgebras and Representation Theory
Volume8
Issue number4
DOIs
Publication statusPublished - Oct 2005

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Frobenius
If and only if
Algebra
Hopf Algebra
Semisimple
Necessary Conditions
Sufficient Conditions
Generalization

Keywords

  • (Quasi-)Frobenius extension
  • Hopf algebroid
  • Integral
  • Maschke theorem

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Integral theory for Hopf algebroids. / Böhm, G.

In: Algebras and Representation Theory, Vol. 8, No. 4, 10.2005, p. 563-599.

Research output: Contribution to journalArticle

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