Lie type algebras with an automorphism of finite order

Lie Algebras of Finite and Affine Type

Nottingham Lie Algebras with Diamonds of Finite Type

We study a class of positively graded Lie algebras with a pattern of homogeneous components similar to that of the graded Lie algebra associated to the Nottingham group with respect to its lower central series.

Classification of Lie Subalgebras up to an Inner Automorphism

In this paper, a useful classification of all Lie subalgebras of a given Lie algebraup to an inner automorphism is presented. This method can be regarded as animportant connection between differential geometry and algebra and has many applications in different fields of mathematics. After main results, we have applied this procedure for classifying the Lie subalgebras of some examples of Lie al...

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...

Lie-type higher derivations on operator algebras

 Motivated by the intensive and powerful works concerning additive‎ ‎mappings of operator algebras‎, ‎we mainly study Lie-type higher‎ ‎derivations on operator algebras in the current work‎. ‎It is shown‎ ‎that every Lie (triple-)higher derivation on some classical operator‎ ‎algebras is of standard form‎. ‎The definition of Lie $n$-higher‎ ‎derivations on operator algebras and related pot...