Hopf algebroids with bijective antipodes: Axioms, integrals, and duals

Gabriella Böhm, Kornél Szlachányi

Research output: Contribution to journalArticle

47 Citations (Scopus)

Abstract

Motivated by the study of depth 2 Frobenius extensions, we introduce a new notion of Hopf algebroid. It is a 2-sided bialgebroid with a bijective antipode which connects the two, left and right handed, structures. While all the interesting examples of the Hopf algebroid of J.H. Lu turn out to be Hopf algebroids in the sense of this paper, there exist simple examples showing that our definition is not a special case of Lu's. Our Hopf algebroids, however, belong to the class of X L-Hopf algebras proposed by P. Schauenburg. After discussing the axioms and some examples, we study the theory of non-degenerate integrals in order to obtain duals of Hopf algebroids.

Original languageEnglish
Pages (from-to)708-750
Number of pages43
JournalJournal of Algebra
Volume274
Issue number2
DOIs
Publication statusPublished - Apr 15 2004

ASJC Scopus subject areas

  • Algebra and Number Theory

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