Homology, Homotopy and Applications

Volume 10 (2008)

Number 2

Partial magmatic bialgebras

Pages: 59 – 81

DOI: http://dx.doi.org/10.4310/HHA.2008.v10.n2.a3

Authors

Emily Burgunder (Université Montpellier II, Montpellier, France)

Ralf Holtkamp (Fakultät für Mathematik, Ruhr-Universität, Bochum, Germany)

Abstract

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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