2002/10/18 by Michel Goze, Goze, Michel, Elisabeth Remm +1
Mathematics · #Category Theory (math.CT) #Differential Geometry (math.DG) #FOS: Mathematics #Lie-admissible algebras. Vinberg algebras. PreLie algebras. Operads. Cohomology #Rings and Algebras (math.RA) #math.CT #math.DG #math.RA
paper · pdf · doi:10.48550/arxiv.math/0210291
20 pages
arxiv created 2002/10/18 · arxiv updated 2009/11/30
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.