A 2-step nilpotent Lie algebra n is called nonsingular if ad(X): n --> [n,n] is onto for any X not in [n,n]. We explore nonsingular algebras in several directions, including the classification problem (isomorphism invariants), ...

Given a sequence d~ = (d1, . . . , dk) of natural numbers, we consider the Lie subalgebra h of gl(d, F), where d = d1 + · · · + dk and F is a field of characteristic 0, generated by two block upper triangular matrices D ...

We generalize a result on the Heisenberg Lie algebra that gives restrictions to possible Lie bialgebra cobrackets on 2-step nilpotent algebras with some additional properties. For the class of 2-step nilpotent Lie algebras ...

Let N be a nilpotent Lie group and K a compact subgroup of the automorphism group Aut(N) of N. It is well-known that if (K⋉ N, K) is a Gelfand pair then N is at most 2-step nilpotent Lie group. The notion of Gelfand pair ...

Given an algebraically closed field F of characteristic 0 and an F-vector space V, let L(V) = V⊕Λ2(V) denote the free 2-step nilpotent Lie algebra associated to V. In this paper, we classify all uniserial representations ...

This paper deals with naturally reductive pseudo-Riemannian 2- step nilpotent Lie groups for which the metric is invariant under a left action. The case of nondegenerate center is characterized as follows. The simply ...

In this article we show that the only 2-step nilpotent Lie groups which carry a non-degenerate left invariant Killing–Yano 2-form are the complex Lie groups. In the case of 2-step nilpotent complex Lie groups arising from ...

For a real, non-singular, 2-step nilpotent Lie algebra n, the group Aut(n)/ Aut0(n), where Aut0(n) is the group of automorphisms which act trivially on the center, is the direct product of a compact group with the 1-dimensional ...

Abstract: We generalize a result on the Heisenberg Lie algebra that gives restrictions to possible Lie bialgebra cobrackets on 2-step nilpotent algebras with some additional properties. For the class of 2-step nilpotent ...

The goal of this paper is the study of the integrability of the geodesic flow on k-step nilpotent Lie groups, k=2,3, when equipped with a leftinvariant metric. Liouville integrability is proved in low dimensions. Moreover, ...