Let G be the adjoint group of a simple Lie algebra g, and let KC ! Aut(pC) be the complexi ed isotropy representation at the identity coset of the corresponding symmetric space. If e 2 pC is nilpotent, we consider the centralizer of e in KC. We show that the conjugacy classes of the component group of this centralizer can be described in terms generalizing the Bala-Carter classi cation of nilpo...

The main part of this paper contains a description of a nilpotent quotient algorithm for L-presented groups and a report on applications of its implementation in the computer algebra system GAP. The appendix introduces two new infinite series of L-presented groups. Apart from being of interest in their own right, these new L-presented groups serve as examples for applications of the nilpotent q...

An absolute parallelism for $2$-nondegenerate CR manifolds $M$ of hypersurface type was recently constructed independently by Isaev-Zaitsev, Medori-Spiro, and Pocchiola in the minimal possible dimension ($\dim M=5$), $\dim M=7$ certain cases first author. We develop a bigraded analog Tanaka's prolongation procedure to construct canonical these structures arbitrary (odd) with Levi kernel admissi...

Leibniz algebras are a non-anticommutative version of Lie algebras. They play an important role in different areas mathematics and physics have attracted much attention over the last thirty years. In this paper we investigate whether conditions such as being algebra, cyclic, simple, semisimple, solvable, supersolvable or nilpotent algebra preserved by lattice isomorphisms.

In this note we compute Leibniz algebra deformations of the 3-dimensional nilpotent Lie algebra n3 and compare it with its Lie deformations. It turns out that there are 3 extra Leibniz deformations. We also describe the versal Leibniz deformation of n3 with the versal base.

We construct an explicit set of algebraically independent generators for the center of the universal enveloping algebra of the centralizer of a nilpotent matrix in the general linear Lie algebra over a field of characteristic zero. In particular, this gives a new proof of the freeness of the center, a result first proved by Panyushev, Premet and Yakimova.

We prove that the maximal nilpotent subalgebra of a Kac-Moody Lie algebra has a (essentially, unique) Euclidean metric with respect to which the Laplace operator in the chain complex is scalar on each component of a given degree. Moreover, both the Lie algebra structure and the metric are uniquely determined by this property.

Two groups are said to have the same nilpotent genus if they have the same nilpotent quotients. We answer four questions of Baumslag concerning nilpotent completions. (i) There exists a pair of finitely generated, residually torsion-free-nilpotent groups of the same nilpotent genus such that one is finitely presented and the other is not. (ii) There exists a pair of finitely presented, residual...

With slight modifications in the zero modes contributions, the positive and negative screening currents for the quantum deformed W -algebra Wq,p(g) can be put together to form a single algebra which can be regarded as an elliptic deformation of the universal enveloping algebra of ĝ, where g is any classical simply-laced Lie algebra. Recently, various deformations of the classical and quantum Vi...

this work is a continuation of [a‎. ‎o‎. ‎asar‎, ‎‎‎on infinitely generated groups whose proper subgroups are solvable‎, ‎{em j‎. ‎algebra}‎, ‎{bf 399} (2014) 870-886.]‎, ‎where it was shown‎ ‎that a perfect infinitely generated group whose proper subgroups‎ are solvable and in whose homomorphic images normal closures of ‎finitely generated subgroups are residually nilpotent is a fitting‎‎$p$-g...