The goal of the current work is to introduce Lie algebras and to present their basic properties concerning subalgebras, homomorphisms and representations. We will also define nilpotent and solvable Lie algebras and prove ...

Let K be a field of characteristic zero, g be a finite dimensional K-Lie algebra and let A be a finite dimensional associative and commutative K-algebra with unit. We describe the structure of the Lie algebra of derivations ...

In the present work, binary-Lie, assocyclic, and binary (-1,1) algebras are studied. We prove that, for every assocyclic algebra A, the algebra A(-) is binary-Lie. We find a simple non-Malcev binary-Lie superalgebra T that ...

In the present work, binary-Lie, assocyclic, and binary (-1,1) algebras are studied. We prove that, for every assocyclic algebra A, the algebra A - is binary-Lie. We find a simple non-Malcev binary-Lie superalgebra T that ...

Let M(n) be the class of all multiloop algebras of finite dimensional simple Lie algebras relative to n-tuples of commuting finite order automorphisms. It is a classical result that M(n) the class of all derived algebras ...

The generalizations of Lie algebras appeared in the modern mathematics and mathematical physics. In this paper we consider recent developments and remaining open problems on the subject. Some of that developments have been ...

Let L and H be two Lie algebras and UL and UH be their respective universal enveloping algebras. The isomorphism problem for universal enveloping algebras of Lie algebras asks us to determine under what conditions the ...