Lie-admissible algebras and operads
Rings and Algebras
2007-05-23 v1 Category Theory
Differential Geometry
Abstract
A Lie-admissible algebra gives by anticommutativity a Lie algebra. In this work we study remarkable classes of Lie-admissible algebras such as Vinberg, PreLie algebras. We compute the corresponding binary quadratic operads and study their Koszul duality. Considering Lie algebras as Lie-admissible algebras we can define for each Lie algebra a cohomology with values in a Lie-admissible module. This permits to study some deformations of Lie algebras in the category of Lie-admissible algebras. Lastly we study the tensor product between these operads and their dual operads. As application we construct new classes of Vinberg algebras.
Cite
@article{arxiv.math/0210291,
title = {Lie-admissible algebras and operads},
author = {Michel Goze and Elisabeth Remm},
journal= {arXiv preprint arXiv:math/0210291},
year = {2007}
}
Comments
20 pages