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arXiv · 1309.5318

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

Loïc Foissy
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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.

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Loïc Foissy. 2014-12-23. A prelie algebra associated to a linear endomorphism and related algebraic structures. https://arxiv.org/abs/1309.5318

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