Bialgebroids, ${\times }_A$-bialgebras and duality

Abstract

An equivalence between Lu's bialgebroids, Xu's bialgebroids with an anchor and Takeuchi's ${\times }_A$-bialgebras is explicitly proven. A new class of examples of bialgebroids is constructed. A (formal) dual of a bialgebroid, termed bicoalgebroid, is defined. A weak Hopf algebra is shown to be an example of such a bicoalgebroid.

16 pages, LaTeX; more concise presentation; Theorem 4.1 improved; final version to appear in J. Algebra