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Lie-admissible algebras and operads

Michel Goze·Elisabeth Remm
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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.

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Michel Goze, Elisabeth Remm. 2002-10-18. Lie-admissible algebras and operads. https://arxiv.org/abs/math/0210291

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