Lie-admissible algebras and operads

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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.
20 pages

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Rings and Algebras, Category Theory, Differential Geometry, Lie-admissible algebras. Vinberg algebras. PreLie algebras. Operads. Cohomology

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http://salesiana.dossiersoluciones.com/handle/123456789/65351

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0210291
 http://arxiv.org/abs/math/0210291

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arXiv