Given a Lie algebra g over a field of characteristic zero k, let μ(g) = min{dimπ : π is a faithful representation of g}. Let hm be the Heisenberg Lie algebra of dimension 2m + 1 over k and let k[t] be the polynomial algebra in one variable. Given m ∈ N and p ∈ k[t], let hm,p = hm ⊗ k[t]/(p) be the current Lie algebra associated to hm and k[t]/(p), where (p) is the principal ideal in k[t] genera...

This paper shows a new computational method to obtain filiform Lie algebras, which is based on the relation between some known invariants of these algebras and the maximal dimension of their abelian ideals. Using this relation, the law of each of these algebras can be completely determined and characterized by means of the triple consisting of its dimension and the invariants z1 and z2. As exam...

We construct a generator system of the annihilator of a generalized Verma module of a classical reductive Lie algebra induced from a character of a parabolic subalgebra as an analogue of the minimal polynomial of a matrix. In a classical limit it gives a generator system of the defining ideal of any semisimple co-adjoint orbit of the Lie algebra. We also give some applications to integral geome...

In this paper we consider Q the class of solvable Lie algebras L with the following property: if A is a subalgebra of L, then Φ(A) ⊆ Φ(L) (where Φ(L) denotes the Frattini subalgebra of L;that is Φ(L) is the intersection of all maximal subalgebras of L). The class Q is shown to contain all solvable Lie algebras whose derived algebra is nilpotent. Necessary conditions are found such that an ideal...

Tetra-n-butylammonium bromide forms the title semi-clathrate hydrate crystal, C16H36N+.Br-.38H2O, under atmospheric pressure. The cation and anion lie at sites with mm symmetry and seven water molecules lie at sites with m symmetry in space group Pmma. Br- anions construct a cage structure with the water molecules. Tetra-n-butylammonium cations are disordered and are located at the centre of fo...

We study free centre-by-metabelian Lie algebras over a field of characteristic 2. By using homological methods, we determine the dimensions of the fine homogeneous components of the second-derived algebra. In conjunction with earlier results by Mansuroǧlu and the second author, this leads to a complete description of the additive structure of the second-derived ideal in the free centre-by-metab...