Mathematics – Quantum Algebra
Scientific paper
2003-02-26
J. Algebra 274 (2004) 708-750
Mathematics
Quantum Algebra
31 pages LaTeX2e file
Scientific paper
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 $\times_L$-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.
B"ohm Gabriella
Szlach'anyi Korn'el
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