Journal of Lie Theory 17 (2007), No. 3, 633--668
Copyright Heldermann Verlag 2007
New Applications of Graded Lie Algebras to Lie Algebras, Generalized Lie Algebras, and Cohomology
Georges Pinczon
Institut de Mathématiques, Université de Bourgogne, B.P. 47870, 21078 Dijon, France
gpinczon@u-bourgogne.fr
Rosane Ushirobira
Institut de Mathématiques, Université de Bourgogne, B.P. 47870, 21078 Dijon, France
rosane@u-bourgogne.fr
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.
Keywords: 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.
MSC: 17B70, 17B05, 17B20, 17B56, 17B60, 17B65
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