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- W4301403762 abstract "We attach to any linear endomorphism f of any vector space V a structure of prelie algebra on the shuffle algebra T(V); we describe its enveloping algebra, the dual Hopf algebra and the associated group of characters. For f=Id_V, we find the algebra of formal diffeomorphisms, seen as a subalgebra of the Connes-Kreimer Hopf algebra of rooted trees in the context of QFT; for other well-chosen f, we obtain the groups of Fliess operators in Control Theory. An algebraic structures of these Com-Prelie Hopf algebras is carried out: gradations, group of automorphisms, subobject generated by V, etc." @default.
- W4301403762 created "2022-10-05" @default.
- W4301403762 creator A5064298910 @default.
- W4301403762 date "2013-09-20" @default.
- W4301403762 modified "2023-10-03" @default.
- W4301403762 title "A prelie algebra associated to a linear endomorphism and related algebraic structures" @default.
- W4301403762 doi "https://doi.org/10.48550/arxiv.1309.5318" @default.
- W4301403762 hasPublicationYear "2013" @default.
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