Partial magmatic bialgebras

A partial magmatic bialgebra, or $(T; S)$-magmatic bialgebra, where $T ⊂ S$ are subsets of $\mathbb{N} _{\geq 2}$, is a vector space endowed with an $n$-ary operation for each $n ∈ S$ and an $m$-ary co-operation for each $m ∈ T$ satisfying some compatibility and unitary relations. We prove an analogue of the Poincaré-Birkhoff-Witt theorem for these partial magmatic bialgebras.

Keywords

generalized bialgebra, Hopf algebra, Cartier-Milnor-Moore theorem, Poincaré-Birkhoff-Witt theorem, operad, magma, non-associative algebra

2010 Mathematics Subject Classification

18D50

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Published 1 January 2008