New applications of graded Lie algebras to Lie algebras, generalized Lie algebras and cohomology

Georges Pinczon (1) , Rosane Ushirobira (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

We give new applications of graded Lie algebras to: identities of standard polynomials, deformation theory of quadratic Lie algebras, cyclic cohomology of quadratic Lie algebras, $2k$-Lie algebras, generalized Poisson brackets and so on.

Mots clés: standard polynomial; Deformation theory; graded Lie algebras; Gerstenhaber bracket; Gerstenhaber-Nijenhuis bracket; Schouten bracket; super Poisson brackets; quadratic Lie algebra; cyclic cohomology; 2k-Lie algebras; standard polynomial.

Domaines: Théorie des représentations [math.RT]

Georges Pinczon, Rosane Ushirobira. New applications of graded Lie algebras to Lie algebras, generalized Lie algebras and cohomology. Journal of Lie Theory, 2007, 17 (3), pp.633-668. ⟨hal-00439228⟩