This paper is a sequel to the paper [7] in which generalized Cartan type S Lie algebras tzS(A, T, φ) over a field F of characteristic 0 were studied. We have tried to make this paper independent of other papers. So in Section 2, we give a description of relevant Lie algebras and some basic facts which will be used in this paper. In Section 3 we introduce a class of Lie algebras which are subalg...

Nongraded infinite-dimensional Lie algebras appeared naturally in the theory of Hamiltonian operators, the theory of vertex algebras and their multi-variable analogues. They play important roles in mathematical physics. This survey article is written based on the author’s seminar talks on nongraded infinite-dimensional simple Lie algebras. The key constructional ingredients of our Lie algebras ...

the aim of this paper is to show that under some mild conditions a functional equation of multiplicative (; )-derivation is superstable on standard operator algebras. furthermore, we prove that this generalized derivation can be a continuous and an inner (; )- derivation.

We consider the Lie algebra of derivations of a zero dimensional local complex algebra. We describe an inequality involving the embedding dimension, the order, and the first deviation that forces this Lie algebra to be solvable. Our result was motivated by and generalizes the solvability of the Yau algebra of an isolated hypersurface singularity.

The Lie algebras of trace-zero derivations of Heisenberg-type groups are explicitly characterized, along with the connected component of their groups of measure preserving automorphisms. We establish a general criterion on properties of the stabilizer of a lattice in a simply connected nilpotent Lie group and apply it to the full family of H -type Lie groups. A necessary condition for the exist...

We shall describe some Lie algebras of Kac-Moody type, construct their double extensions, central and by derivations; in some cases, the corresponding Lie groups will also be constructed. The case of Lie algebra of unimodular vector fields will be studied in more details. We use the linear Poisson structure on their regular duals to construct generalizations of some infinite dimensional hamilto...