Lie algebras with finite-dimensional polynomial centralizer

On permutably complemented subalgebras of finite dimensional Lie algebras

Let $L$ be a finite-dimensional Lie algebra. We say a subalgebra $H$ of $L$ is permutably complemented in $L$ if there is a subalgebra $K$ of $L$ such that $L=H+K$ and $Hcap K=0$. Also, if every subalgebra of $L$ is permutably complemented in $L$, then $L$ is called completely factorisable. In this article, we consider the influence of these concepts on the structure of a Lie algebra, in partic...

Computations in finite-dimensional Lie algebras

This paper describes progress made in context with the construction of a general library of Lie algebra algorithms, called ELIAS (Eindhoven LIe Algebra System), within the computer algebra package GAP. A first sketch of the package can be found in Cohen and de Graaf[1]. Since then, in a collaborative effort with G. Ivanyos, the authors have continued to develop algorithms which were implemented...

Classification of Finite-dimensional Semisimple Lie Algebras

Every finite-dimensional Lie algebra is a semi-direct product of a solvable Lie algebra and a semisimple Lie algebra. Classifying the solvable Lie algebras is difficult, but the semisimple Lie algebras have a relatively easy classification. We discuss in some detail how the representation theory of the particular Lie algebra sl2 tightly controls the structure of general semisimple Lie algebras,...

A Note on Finite Dimensional Subideals of Lie Algebras

1.1 We prove that: Over any field I of characteristic p > 0, there exists an infinite dimensional Lie algebra which is the join of two (p + l)-dimensional and nilpotent (of class exactly p) subideals. A result of Hartley ([2; p. 259, theorems 2 and 5]) states that over any field of characteristic zero, the join of a pair of finite dimensional (resp. finite dimensional and nilpotent) subideals i...

Infinite-dimensional Lie algebras