Bialgebroids, $\times_{A}$-bialgebras and duality

Gigel Militaru; Tomasz Brzezinski

Bialgebroids, $\times_{A}$-bialgebras and duality

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arxiv math/0012164 v2 pith:KNVLUNOM submitted 2000-12-18 math.QA math.RA

Tomasz Brzezinski , Gigel Militaru This is my paper

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keywords bialgebroidsbialgebrasbicoalgebroidtimesalgebraanchorbialgebroidclass

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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.

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Examples of scalar extension Hopf algebroids over a universal enveloping algebra
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For a finite-dimensional Lie algebra g, U(g) is a braided commutative Yetter-Drinfeld module algebra over any Hopf algebra H containing the adjoint matrix coefficients, making H smash U(g) a scalar extension Hopf alge...

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