A formula for the logarithm of the KZ associator.
A note on automorphism group of an n-generator nilpotent lie algebra
Algebraic combinatorics related to the free Lie algebra.
Algebraic setup of non-strict multiple zeta values
Algèbres de Lie libres associées a un système de Pfaff.
By using an invariant related to free Lie algebras, we give a criterion of non existence of isomorphism for the Pfaffian systems.
Asymptotic Behaviour of Colength of Varieties of Lie Algebras
This project was partially supported by RFBR, grants 99-01-00233, 98-01-01020 and 00-15-96128.We study the asymptotic behaviour of numerical characteristics of polynomial identities of Lie algebras over a field of characteristic 0. In particular we investigate the colength for the cocharacters of polynilpotent varieties of Lie algebras. We prove that there exist polynilpotent Lie varieties with exponential and overexponential colength growth. We give the exact asymptotics for the colength of a product...
Automorphisms of free nilpotent associative algebras.
Computational techniques for PI-algebras
Computing the test rank of a free solvable Lie algebra.
Cyclotomic identities, Lie superalgebras and bicharacters. (Identité cyclotomique, superalgèbres de Lie et bicaractères.)
Defining relations for classical Lie algebras of polynomial vector fields.
Defining relations for classical Lie superalgebras without Cartan matrices.
Determination of endomorphisms of free metabelian Lie algebras.
Different methods for the study of obstructions in the schemes of Jacobi
In this paper the problem of obstructions in Lie algebra deformations is studied from four different points of view. First, we illustrate the method of local ring, an alternative to Gerstenhaber’s method for Lie deformations. We draw parallels between both methods showing that an obstruction class corresponds to a nilpotent local parameter of a versal deformation of the law in the scheme of Jacobi. Then, an elimination process in the global ring, which defines the scheme, allows us to obtain nilpotent...
Elimination of generators in partially commutative structures. (Élimination de générateurs dans les structures partiellement commutatives.)
Endomorphisms of free metabelian Lie algebras which preserve orbits.
Enumeration of maximal subalgebras in free restricted Lie algebras.
Finely homogeneous computations in free Lie algebras.
La décomposition en poids des algèbres de Hopf
Si est une algèbre de Hopf commutative ou cocommutative et connexe, les puissances de convolution et le logarithme, au sens du produit de convolution, du morphisme identité de satisfont à diverses identités algébriques. L’algèbre de Hopf admet en particulier une décomposition en poids sous l’action des morphismes , dont nous étudions les propriétés.
Lie powers of infinite-dimensional modules.