Search results for "standard polynomial."
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Nambu structures and super-theorem of Amitsur-Levitzki
2004
In this thesis, we establish new polynomial identities in a non commutative combinatorial framework. In the first part, we present new Nambu-Lie structures by classifying all (n-1)-structures in \R^n and we give a method for defining all-order brackets in Lie algebras. We are able to quantify one of our structures, thanks to standard polynomials and even Clifford algebras. In the second part of our work, we generalize the notion of standard polynomials to graded algebras, and we prove an Amitsur-Levitzki type theorem for the Lie superalgebras \osp(1,2n) inspired by Kostant's cohomological interpretation of the classical theorem. We give super versions of properties and results needed in Kos…
New applications of graded Lie algebras to Lie algebras, generalized Lie algebras and cohomology
2007
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.