SUANMALI, SUTHATHIP. On the Relationship between the Class of a Lie Algebra and the Classes of its Subalgebras. (Under the direction of Ernie L. Stitzinger.) A classical nilpotency result considers finite p-groups whose proper subgroups all have class bounded by a fixed number n. We consider the analogous property in nilpotent Lie algebras. In particular, we investigate whether this condition p...

The observations in this talk come from a paper in preparation by A. Čap, M. Cowling, F. De Mari, M. Eastwood and R. McCallum about the Heisenberg group and the flag manifold, and more general papers by Cowling, De Mari, A. Korányi and H.M. Reimann, one published [?] and one in preparation, as well as papers by McCallum (in preparation) and B. Warhurst [?]. A Carnot group N is a connected, simp...

The Heisenberg Lie Group is the most frequently used model for studying representation theory of groups. This group modular-noncompact and its algebra nilpotent. elements can be expressed in form matrices size 3×3. Another specialty also inherited by three-dimensional called algebra. whose Algebra extended to dimension 2n+1 generalized it denoted H h_n. In this study, surjectiveness exponential...

Many work was done for filiform Lie algebras defined by M. Vergne [8]. An interesting fact is that this algebras are obtained by deformations of the filiform Lie algebra Ln,m. This was used for classifications in [4]. Like filiform Lie algebras, filiform Lie superalgebras are obtained by nilpotent deformations of the Lie superalgebra Ln,m. In this paper, we recall this fact and we study even co...

This paper develops a method for constructing nilpo-tent approximations for local representations of invariant systems on matrix Lie groups via a simple operation on the structure constants of the associated Lie algebra. The crucial role such nilpotent approximations play for the problem of feedback nilpotentization is discussed. The presented ideas are illustrated with an example modeling the ...

Locally extended affine Lie algebras were introduced by Morita and Yoshii in [J. Algebra 301(1) (2006), 59-81] as a natural generalization of extended affine Lie algebras. After that, various generalizations of these Lie algebras have been investigated by others. It is known that a locally extended affine Lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...

— Let g be a finite dimensional complex reductive Lie algebra and S(g) its symmetric algebra. The nilpotent bicone of g is the subset of elements (x, y) of g×g whose subspace generated by x and y is contained in the nilpotent cone. The nilpotent bicone is naturally endowed with a scheme structure, as nullvariety of the augmentation ideal of the subalgebra of S(g) ⊗C S(g) generated by the 2-orde...

We classify the nilpotent Lie algebras of real dimension eight and minimal center that admit a complex structure. Furthermore, for every such algebra g, we describe space structures on g up to isomorphism. As an application, having non-trivial abelian J-invariant ideal are classified dimensions.

We compare by a very elementary approach the second adjoint and trivial Leibniz cohomology spaces of a Lie algebra to the usual ones. Examples are given of coupled cocycles. Some properties are deduced as to Leibniz deformations. We also consider the class of Lie algebras for which the Koszul 3-form is zero, and prove that it contains all quotients of Borel subalgebras, or of their nilradicals,...