# Infinite magmatic bialgebras

Research paper by Emily Burgunder

Indexed on: 04 Jan '06Published on: 04 Jan '06Published in: Mathematics - Rings and Algebras

#### Abstract

An infinite magmatic bialgebra is a vector space endowed with an n-ary operation, and an n-ary cooperation, for each n, verifying some compatibility relations. We prove a rigidity theorem, analogue to the Hopf-Borel theorem for commutative bialgebras: any connected infinite magmatic bialgebra is of the form $Mag^\infty(Prim H)$, where $Mag^\infty(V)$ is the free infinite magmatic algebra over the vector space V.