Lie-admissible algebras and operads. (Q1427382)

An algebra \((A,\mu)\) is called Lie-admissible if \(\mu(X,Y)-\mu(Y,X)\) gives a Lie bracket. Associative algebras, Vinberg (or left symmetric) algebras, pre-Lie (or right symmetric) algebras and Lie algebras are examples. The corresponding binary quadratic operads are computed in each case. The cohomology of Lie-admissible algebras is considered. That gives the Lie-admissible cohomology of Lie algebras with values in a Lie-admissible module. At the end the authors study deformations of Lie algebras in the classes of Lie-admissible algebras.