A prelie algebra associated to a linear endomorphism and related algebraic structures
Rings and Algebras
2014-12-24 v2
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.
Keywords
Cite
@article{arxiv.1309.5318,
title = {A prelie algebra associated to a linear endomorphism and related algebraic structures},
author = {Loïc Foissy},
journal= {arXiv preprint arXiv:1309.5318},
year = {2014}
}
Comments
Final version. To be pubished in European Journal of Mathematics