Covering-Avoidance for Satured Formations of Solvable Lie Algebras.
Darstellungen auflösbarer Lie-p-Algebren.
Degenerations of nilpotent Lie algebras.
Derivation algebras of certain nilpotent Lie algebras.
Determination of endomorphisms of free metabelian Lie algebras.
Determination of invariant inner product on seven dimensional nilpotent 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...
Dilations and gauges on nilpotent Lie groups
Directed pseudo-graphs and Lie algebras over finite fields
The main goal of this paper is to show an application of Graph Theory to classifying Lie algebras over finite fields. It is rooted in the representation of each Lie algebra by a certain pseudo-graph. As partial results, it is deduced that there exist, up to isomorphism, four, six, fourteen and thirty-four -, -, -, and -dimensional algebras of the studied family, respectively, over the field . Over , eight and twenty-two - and -dimensional Lie algebras, respectively, are also found. Finally,...
Dual topology of a nilpotent Lie group
Exotic Deformations of Calabi-Yau Manifolds
We introduce Quantum Inner State manifolds (QIS manifolds) as (compact) -dimensional symplectic manifolds endowed with a -tamed almost complex structure and with a nowhere vanishing and normalized section of the bundle satisfying the condition .We study the moduli space of QIS deformations of a given Calabi-Yau manifold, computing its tangent space and showing that is non obstructed. Finally, we present several examples of QIS manifolds.
Finite-dimensional Lie subalgebras of algebras with continuous inversion
We investigate the finite-dimensional Lie groups whose points are separated by the continuous homomorphisms into groups of invertible elements of locally convex algebras with continuous inversion that satisfy an appropriate completeness condition. We find that these are precisely the linear Lie groups, that is, the Lie groups which can be faithfully represented as matrix groups. Our method relies on proving that certain finite-dimensional Lie subalgebras of algebras with continuous inversion commute...
Gelfand-Kirillor Dimension for non-Associative Algebras
Gel'fand-Kirillov dimension for algebras associated with the Weyl algebra
Generator and relation ranks for finite-dimensional nilpotent Lie algebras.
Graded nilpotent Lie algebras in low dimensions.
Graphs associated with nilpotent Lie algebras of maximal rank.
In this paper, we use the graphs as a tool to study nilpotent Lie algebras. It implies to set up a link betwcen graph theory and Lie theory. To do this, it is already known that every nilpotent Lie algebra of maximal rank is associated with a generalized Cartan matrix A and it ils isomorphic to a quotient of the positive part n+ of the KacMoody algebra g(A). Then, if A is affine, we can associate n+ with a directed graph (from now on, we use the term digraph) and we can also associate a subgraph...
Ideals of free metabelian Lie algebras and primitive elements.
Integral structures on H-type Lie algebras.
Invariant cones in solvable Lie algebras.