Partial magmatic bialgebras

Mathematics – Rings and Algebras

Scientific paper

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Revised version, after suggestions of the anonymous referee, 20 pages

Scientific paper

A partial magmatic bialgebra, (T;S)-magmatic bialgebra where T \subset S are
subsets of the set of positive integers, is a vector space endowed with an
n-ary operation for each n in S and an m-ary co-operation for each m in T
satisfying some compatibility and unitary relations. We prove an analogue of
the Poincar\'e-Birkhoff-Witt theorem for these partial magmatic bialgebras.

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