On solvability of Lie rings with an automorphism of finite order.
On Solvable Generalized Calabi-Yau Manifolds
We give an example of a compact 6-dimensional non-Kähler symplectic manifold that satisfies the Hard Lefschetz Condition. Moreover, it is showed that is a special generalized Calabi-Yau manifold.
On some classes of nilpotent Leibniz algebras.
On the basic algebraic operations in solvable Lie groups.
On the Characterization of Primitive Ideals in Enveloping Algebras.
On the cohomology of nilpotent Lie algebras
On the Derived Length of Solvable Lie Algebras.
On the homology of free nilpotent Lie algebras.
On the joint spectral radius of a nilpotent Lie algebra of matrices
For a complex nilpotent finite-dimensional Lie algebra of matrices, and a Jordan-Hölder basis of it, we prove a spectral radius formula which extends a well-known result for commuting matrices.
On the multiplier of a Lie algebra.
On the nilpotency of certain subalgebras of Kac-Moody Lie algebras.
On the nilpotent residuals of all subalgebras of Lie algebras
Let denote the class of nilpotent Lie algebras. For any finite-dimensional Lie algebra over an arbitrary field , there exists a smallest ideal of such that . This uniquely determined ideal of is called the nilpotent residual of and is denoted by . In this paper, we define the subalgebra . Set . Define for . By denote the terminal term of the ascending series. It is proved that if and only if is nilpotent. In addition, we investigate the basic properties of a Lie algebra...
On the spectral set of a solvable Lie algebra of operators.
On the structure of solvable Lie algebras.
Orbits and primitive ideals of solvable 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.
Paramétrisation du dual d'une algèbre de Lie nilpotente
Pour tout groupe de Lie nilpotent réel connexe et simplement connexe, on construit une stratification du dual de l’algèbre de Lie, et on paramètre chaque strate au moyen d’un triplet de fonctions rationnelles à valeurs vectorielles; les valeurs de caractérisent les orbites de la strate et pour chacune de ces orbites, le couple constitue une carte de Darboux.
Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebras
In this paper we give the description of some non-strongly nilpotent Leibniz algebras. We pay our attention to the subclass of nilpotent Leibniz algebras, which is called filiform. Note that the set of filiform Leibniz algebras of fixed dimension can be decomposed into three disjoint families. We describe the pre-derivations of filiform Leibniz algebras for the first and second families and determine those algebras in the first two classes of filiform Leibniz algebras that are non-strongly nilpotent....
Product structures on four dimensional solvable Lie algebras.
Quasispectra of solvable Lie algebra homomorphisms into Banach algebras
We propose a noncommutative holomorphic functional calculus on absolutely convex domains for a Banach algebra homomorphism π of a finite-dimensional solvable Lie algebra 𝔤 in terms of quasispectra σ(π). In particular, we prove that the joint spectral radius of a compact subset in a solvable operator Lie subalgebra coincides with the geometric spectral radius with respect to a quasispectrum.