Displaying similar documents to “Classification of solvable Lie algebras.”

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.

Restricted and quasi-toral restricted Lie-Rinehart algebras

Bing Sun, Liangyun Chen (2015)

Open Mathematics


In this paper, we introduce the definition of restrictable Lie-Rinehart algebras, the concept of restrictability is by far more tractable than that of a restricted Lie-Rinehart algebra. Moreover, we obtain some properties of p-mappings and restrictable Lie-Rinehart algebras. Finally, we give some sufficient conditions for the commutativity of quasi-toral restricted Lie-Rinehart algebras and study how a quasi-toral restricted Lie-Rinehart algebra with zero center and of minimal dimension...

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.

Poisson-Lie groupoids and the contraction procedure

Kenny De Commer (2015)

Banach Center Publications


On the level of Lie algebras, the contraction procedure is a method to create a new Lie algebra from a given Lie algebra by rescaling generators and letting the scaling parameter tend to zero. One of the most well-known examples is the contraction from 𝔰𝔲(2) to 𝔢(2), the Lie algebra of upper-triangular matrices with zero trace and purely imaginary diagonal. In this paper, we will consider an extension of this contraction by taking also into consideration the natural bialgebra structures...