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Article Dans Une Revue European Journal of Mathematics Année : 2015

A prelie algebra associated to a linear endomorphism and related algebraic structures

Résumé

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.
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Dates et versions

hal-00864137 , version 1 (20-09-2013)
hal-00864137 , version 2 (23-12-2014)

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Loïc Foissy. A prelie algebra associated to a linear endomorphism and related algebraic structures. European Journal of Mathematics, 2015. ⟨hal-00864137v2⟩
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