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.

This paper deals with the variety of commutative nonassociative algebras satisfying the identity Lx + γLx3 = 0, γ ∈ K. In [2] it is proved that if γ = 0, 1 then any finitely generated algebra is nilpotent. Here we generalize this result by proving that if γ 6= −1, then any such algebra is locally nilpotent. Our results require characteristic 6= 2, 3.

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.

Questions about nilpotency of groups satisfying Engel conditions have been considered since 1936, when Zorn proved that finite Engel groups are nilpotent. We prove that 4-Engel groups are locally nilpotent. Our proof makes substantial use of both hand and machine calculations.

An MC group is a group in which all chains of centralizers have finite length. In this article, we show that every nilpotent subgroup of an MC group is contained in a definable subgroup which is nilpotent of the same nilpotence class. Definitions are uniform when the lengths of chains are bounded.

We consider a group-theoretic analogue of the classic subset sum problem. It is known that every virtually nilpotent group has polynomial time decidable subset sum problem. In this paper we use subgroup distortion to show that every polycyclic non-virtually-nilpotent group has NP-complete subset sum problem.

The structure of equivariant cohomology in non-abelian localization formulas and topological field theories is discussed. Equivariance is formulated in terms of a nilpotent BRST symmetry, and another nilpotent operator which restricts the BRST cohomology onto the equivariant, or basic sector. A superfield formulation is presented and connections to reducible (BFV) quantization of topological Ya...

We consider the shape of balls for nilpotent Lie groups endowed with a left invariant Riemannian or sub-Riemannian metric. We prove that when the algebra is graded these balls are homeomorphic to the standard Euclidean ball. For two-step nilpotent groups we show that the intersections of the ball with the central cosets are star-shaped, and in special cases convex.

We formulate a lattice theoretical Jordan normal form theorem for certain nilpotent lattice maps satisfying the so called JNB conditions. As an application of the general results, we obtain a transparent Jordan normal base of a nilpotent endomorphism in a finitely generated semisimple module.

We give a new framework for the construction of homogeneous nilpotent groups and rings which goes a long way toward unifying the two cases, and enables us to extend previous constructions, producing a variety of new examples. In particular we find ingredients for the manufacture of 2No homogeneous nilpotent groups "in nature".