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Infinite magmatic bialgebras

Emily Burgunder
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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.

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Emily Burgunder. 2006-01-04. Infinite magmatic bialgebras. https://arxiv.org/abs/math/0601068

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