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...

Let g be a complex simple Lie algebra. Fix a Borel subalgebra b and a Cartan subalgebra t ⊂ b. The nilpotent radical of b is denoted by u. The corresponding set of positive (resp. simple) roots is ∆ (resp. Π). An ideal of b is called ad-nilpotent, if it is contained in [b, b]. The theory of ad-nilpotent ideals has attracted much recent attention in the work of Kostant, Cellini-Papi, Sommers, an...

We consider the two generalizations of lamplighter groups: automata groups generated by Cayley machines and cross-wired lamplighter groups. For a finite step two nilpotent group with central squares, we study its associated Cayley machine and give a presentation of the corresponding automata group. We show the automata group is a crosswired lamplighter group and does not embed in the wreath pro...

We show that the right ideal of a Novikov algebra generated by square nilpotent subalgebra is nilpotent. also prove [Formula: see text]-graded text] over field with solvable text]-component solvable, where finite additive abelean group and characteristic does not divide order text]. any automorphisms if invariants solvable.

We give the number of nilpotent orbits in the Lie algebras of orthogonal groups under the adjoint action of the groups over F(2(n)). Let G be an adjoint algebraic group of type B, C, or D defined over an algebraically closed field of characteristic 2. We construct the Springer correspondence for the nilpotent variety in the Lie algebra of G.

We study almost contact metric structures on 5-dimensional nilpotent Lie algebras and investigate the class of left invariant almost contact metric structures on corresponding Lie groups. We determine certain classes that a five-dimensional nilpotent Lie group can not be equipped with.

This self-contained paper is part of a series [FF1, FF2] seeking to understand groups of homeomorphisms of manifolds in analogy with the theory of Lie groups and their discrete subgroups. Plante-Thurston proved that every nilpotent subgroup of Diff(S) is abelian. One of our main results is a sharp converse: Diff(S) contains every finitely-generated, torsion-free nilpotent group.

We investigate the irreducibility of the nilpotent Slodowy slices that appear as the associated variety of W -algebras. Furthermore, we provide new examples of vertex algebras whose associated variety has finitely many symplectic leaves. Dedicated to the 60th birthday of Professor Efim Zelmanov