Infinitesimal Hopf algebras (Q2708906)

An infinitesimal bialgebra \(A\) is an associative algebra (not necessarily unital) together with a coassociative coalgebra structure (possibly without counit) such that the comultiplication \(\Delta\) is a derivation of the algebra \(A\) with values on the \(A\)-bimodule \(A\otimes A\). The author defines infinitesimal Hopf algebras, several sufficient conditions for the existence of the antipode are given. In analogy with ordinary Hopf algebra theory, he introduces quasitriangular infinitesimal bialgebras, the corresponding infinitesimal Yang-Baxter equation, bicrossproducts construction and the Drinfeld double for infinitesimal Hopf algebras.NEWLINENEWLINEFor the entire collection see [Zbl 0955.00038].