2003/02/26 by Gabriella B"ohm, Korn'el Szlach'anyi · 3 citations
Mathematics · #math.QA #msc:16W30
published as J. Algebra 274 (2004) 708-750 · 31 pages LaTeX2e file
arxiv created 2003/02/26 · arxiv updated 2009/11/30
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 ×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.