nLab
infinitesimal bialgebra

An infinitesimal bialgebra (abbreviated ϵ\epsilon-bialgebra) over a commutative unital ring kk is a kk-module AA which is equipped with the structures of an associative unital kk-algebra (A,m,η)(A,m,\eta), coassociative counital kk-coalgebra (A,Δ,ϵ)(A,\Delta,\epsilon) and such that the following compatibility condition holds: the comultiplication Δ:AAA\Delta:A\to A\otimes A is a derivation, where AAA\otimes A is equipped with the standard algebra and standard (external) bimodule structure, i.e. Δ(ab)=Δ(a)(1b)+(a1)Δ(b)\Delta(a b) = \Delta(a)(1\otimes b) + (a\otimes 1)\Delta(b).

  • Marcelo Aguiar, On the associative analogues of Lie bialgebras, pdf, Infinitesimal Hopf algebras, pdf

Created on December 18, 2011 at 00:27:17. See the history of this page for a list of all contributions to it.