arXiv subjects

Jean-Michel Oudom

Publications and source records attributed to Jean-Michel Oudom.

2 recordsLinked to original sources

arXiv2008

Deformations of linear Poisson orbifolds

Let $Γ$ be a finite group acting faithfully and linearly on a vector space $V$. Let $T(V)$ ($S(V)$) be the tensor (symmetric) algebra associated to $V$ which has a natural $Γ$ action. We study generalized quadratic relations on the tensor algebra $T(V)\rtimes Γ$. We prove that the quotient algebras of $T(V)\rtimes Γ$ by such relations satisfy PBW property. Such quotient algebras can be viewed as quantizations of linear or constant Poisson structures on $S(V)\rtimes Γ$, and are natural generalizations of symplectic reflection algebras.

math.QA↗

arXiv2004

On the Lie envelopping algebra of a pre-Lie algebra

We construct an associative product on the symmetric module S(L) of any pre-Lie algebra L. Then we proove that in the case of rooted trees our construction is dual to that of Connes and Kreimer. We also show that symmetric brace algebras and pre-Lie algebras are the same. Finally, using brace algebras instead of pre-Lie algebras, we give a similar interpretation of Foissy's Hopf algebra of planar rooted trees.

math.QA↗