We determine which nilpotent orbits in E6 have closures which are normal varieties and which do not. At the same time we are able to verify a conjecture in [14] concerning functions on nonspecial nilpotent orbits for E6.

We give a definition of nilpotent association schemes as a generalization of nilpotent groups and investigate their basic properties. Moreover, for a group-like scheme, we characterize the nilpotency by its character products.

In this work, we present a new classification of nilpotent orbits in a real reductive Lie algebra g under the action of its adjoint group. Our classification generalizes the Bala-Carter classification of the nilpotent orbits of complex semisimple Lie algebras. Our theory takes full advantage of the work of Kostant and Rallis on pC , the “complex symmetric space associated with g”. The Kostant-S...

Abstract. Fix a field F. A zero-nonzero pattern A is said to be potentially nilpotent over F if there exists a matrix with entries in F with zero-nonzero pattern A that allows nilpotence. In this paper we initiate an investigation into which zero-nonzero patterns are potentially nilpotent over F, with a special emphasis on the case that F = Zp is a finite field. As part of this investigation, w...

We give a new characterization of Lusztig’s canonical quotient, a finite group attached to each special nilpotent orbit of a complex semisimple Lie algebra. This group plays an important role in the classification of unipotent representations of finite groups of Lie type. We also define a duality map. To each pair of a nilpotent orbit and a conjugacy class in its fundamental group, the map assi...

Physical limitations of Complementary Metal-Oxide-Semiconductors (CMOS) technology at nanoscale and high cost of lithography have provided the platform for creating Quantum-dot Cellular Automata (QCA)-based hardware. The QCA is a new technology that promises smaller, cheaper and faster electronic circuits, and has been regarded as an effective solution for scalability problems in CMOS technolog...

A Riemannian Einstein solvmanifold (possibly, any noncompact homogeneous Einstein space) is almost completely determined by the nilradical of its Lie algebra. A nilpotent Lie algebra, which can serve as the nilradical of an Einstein metric solvable Lie algebra, is called an Einstein nilradical. Despite a substantial progress towards the understanding of Einstein nilradicals, there is still a la...

Let B be a nilpotent matrix and suppose that its Jordan canonical form is determined by a partition λ. Then it is known that its nilpotent commutator NB is an irreducible variety and that there is a unique partition μ such that the intersection of the orbit of nilpotent matrices corresponding to μ with NB is dense in NB. We prove that map D given by D(λ) = μ is an idempotent map. This answers a...

The subject of left-invariant Ricci soliton metrics on nilpotent Lie groups has enjoyed quite a bit of attention in the past several years. These metrics are intimately related to left-invariant Einstein metrics on non-unimodular solvable Lie groups. In fact, a classification of one is equivalent to a classification of the other. In this note, we focus our attention on nilpotent Lie groups and ...

A nilpotent quotient algorithm for finitely presented Lie rings over Z (LIENQ) is described. The paper studies the graded and non-graded cases separately. The algorithm computes the so-called nilpotent presentation for a finitely presented, nilpotent Lie ring. A nilpotent presentation consists of generators for the abelian group and the products expressed as linear combinations for pairs formed...