Infinitesimal Hopf algebras
نویسندگان
چکیده
Infinitesimal bialgebras were introduced by Joni and Rota [J-R]. An infinitesimal bialgebra is at the same time an algebra and a coalgebra, in such a way that the comultiplication is a derivation. In this paper we define infinitesimal Hopf algebras, develop their basic theory and present several examples. It turns out that many properties of ordinary Hopf algebras possess an infinitesimal version. We introduce bicrossproducts, quasitriangular infinitesimal bialgebras, the corresponding infinitesimal Yang-Baxter equation and a notion of Drinfeld’s double for infinitesimal Hopf algebras.
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