Multizetas, perinomal numbers, arithmetical dimorphy, and ARI/GARI
Nonlinearity of the automorphism groups of some free algebras.
Normal and Normally Outer Automorphisms of Free Metabelian Nilpotent Lie Algebras
2000 Mathematics Subject Classification: 17B01, 17B30, 17B40.Let Lm,c be the free m-generated metabelian nilpotent of class c Lie algebra over a field of characteristic 0. An automorphism φ of Lm,c is called normal if φ(I) = I for every ideal I of the algebra Lm,c. Such automorphisms form a normal subgroup N(Lm,c) of Aut (Lm,c) containing the group of inner automorphisms. We describe the group of normal automorphisms of Lm,c and the quotient group of Aut (Lm,c) modulo N(Lm,c).
On invariants of the action of a finite group on a free Lie algebra.
On Lie powers of regular modules in characteristic 2
On the combinatorial Kashiwara-Vergne conjecture. (Sur la conjecture combinatoire de Kashiwara-Vergne.)
On the homology of free Lie algebras
Given a principal ideal domain of characteristic zero, containing , and a connected differential non-negatively graded free finite type -module , we prove that the natural arrow is an isomorphism of graded Lie algebras over , and deduce thereby that the natural arrow is an isomorphism of graded cocommutative Hopf algebras over ; as usual, stands for free part, for homology, for free Lie algebra, and for universal enveloping algebra. Related facts and examples are also considered....
On the homology of free nilpotent Lie algebras.
On the variety of 3-dimensional Lie algebras.
Outer endomorphisms of free metabelian Lie algebras
2000 Mathematics Subject Classification: 17B01, 17B30, 17B40.Let Fm be the free metabelian Lie algebra of rank m over a field K of characteristic 0. We consider the semigroup IE(Fm) of the endomorphisms of Fm which are identical modulo the commutator ideal of Fm. We describe the factor semigroup of IE(Fm) modulo the congruence induced by the group of inner automorphisms.
-partitions and a multi-parameter Klyachko idempotent.
Polynomial identities in smash products.
Resolutions of singularities of varieties of Lie algebras of dimensions 3 and 4.
Roots of unity as a Lie algebra.
Strictly nontame primitive elements of the free metabelian Lie algebra of rank 3.
Structure theory for the group algebra of the symmetric group, with applications to polynomial identities for the octonions
This is a survey paper on applications of the representation theory of the symmetric group to the theory of polynomial identities for associative and nonassociative algebras. In §1, we present a detailed review (with complete proofs) of the classical structure theory of the group algebra of the symmetric group over a field of characteristic 0 (or ). The goal is to obtain a constructive version of the isomorphism where is a partition of and counts the standard tableaux of shape ....
Sur la représentation adjointe d'une algèbre de Lie libre. II
Soit le noyau de l’application de l’idéal d’augmentation de l’algèbre enveloppante de sur , l’algèbre de Lie libre sur , définie par pour . Si est munie de la représentation adjointe, alors un ensemble de générateurs de comme module sur l’algèbre enveloppante est déterminé en termes des ensembles de Hall relatifs à .
Test sets in free metabelian Lie algebras.
The Hughes subgroup
Let be a group and a prime. The subgroup generated by the elements of order different from is called the Hughes subgroup for exponent . Hughes [3] made the following conjecture: if is non-trivial, its index in is at most . There are many articles that treat this problem. In the present Note we examine those of Strauss and Szekeres [9], which treats the case and arbitrary, and that of Hogan and Kappe [2] concerning the case when is metabelian, and arbitrary. A common proof is...
The hypercentral structure of the group of unitriangular automorphisms of a free metabelian Lie algebra.