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Solvable extensions of a special class of nilpotent Lie algebras

A. Shabanskaya, Gerard Thompson (2013)

Archivum Mathematicum

A pair of sequences of nilpotent Lie algebras denoted by N n , 11 and N n , 19 are introduced. Here n denotes the dimension of the algebras that are defined for n ≥ 6 ; the first term in the sequences are denoted by 6.11 and 6.19, respectively, in the standard list of six-dimensional Lie algebras. For each of N n , 11 and N n , 19 all possible solvable extensions are constructed so that N n , 11 and N n , 19 serve as the nilradical of the corresponding solvable algebras. The construction continues Winternitz’ and colleagues’ program of investigating...

Some division theorems for vector fields

Andrzej Zajtz (1993)

Annales Polonici Mathematici

This paper is concerned with the problem of divisibility of vector fields with respect to the Lie bracket [X,Y]. We deal with the local divisibility. The methods used are based on various estimates, in particular those concerning prolongations of dynamical systems. A generalization to polynomials of the adjoint operator (X) is given.

Some examples of nil Lie algebras

Ivan P. Shestakov, Efim Zelmanov (2008)

Journal of the European Mathematical Society

Generalizing Petrogradsky’s construction, we give examples of infinite-dimensional nil Lie algebras of finite Gelfand–Kirillov dimension over any field of positive characteristic.

Some lagrangian invariants of symplectic manifolds

Michel Nguiffo Boyom (2007)

Banach Center Publications

The KV-homology theory is a new framework which yields interesting properties of lagrangian foliations. This short note is devoted to relationships between the KV-homology and the KV-cohomology of a lagrangian foliation. Let us denote by F (resp. V F ) the KV-algebra (resp. the space of basic functions) of a lagrangian foliation F. We show that there exists a pairing of cohomology and homology to V F . That is to say, there is a bilinear map H q ( F , V F ) × H q ( F , V F ) → V F , which is invariant under F-preserving symplectic diffeomorphisms....

Some necessary and sufficient conditions for nilpotent n -Lie superalgebras

Baoling Guan, Liangyun Chen, Yao Ma (2014)

Czechoslovak Mathematical Journal

The paper studies nilpotent n -Lie superalgebras over a field of characteristic zero. More specifically speaking, we prove Engel’s theorem for n -Lie superalgebras which is a generalization of those for n -Lie algebras and Lie superalgebras. In addition, as an application of Engel’s theorem, we give some properties of nilpotent n -Lie superalgebras and obtain several sufficient conditions for an n -Lie superalgebra to be nilpotent by using the notions of the maximal subalgebra, the weak ideal and the...

Some properties of complex filiform Lie algebras.

F. J. Echarte Reula, J. R. Gómez Martín, J. Núñez Valdés (1992)

Extracta Mathematicae

The purpose of this paper is to study some properties of Filiform Lie Algebras (FLA) and to prove the following theorem: a FLA, of dimension n, is either derived from a Solvable Lie Algebra (SLA) of dimension n+1 or not derived from any LA.

Currently displaying 61 – 80 of 200