This paper is made up of a desire for me to contribute this beautiful field mathematics that I have encountered in recent years. In addition, would like mention am not aware there are papers our Balkans on Lie algebra, although only an introductory part which the near future collaboration with several professors from abroad will do book mother tongue groups and algebras. The main content simila...

‎in this paper‎, ‎using fixed point method‎, ‎we prove the generalized hyers-ulam stability of‎ ‎random homomorphisms in random $c^*$-algebras and random lie $c^*$-algebras‎ ‎and of derivations on non-archimedean random c$^*$-algebras and non-archimedean random lie c$^*$-algebras for‎ ‎the following $m$-variable additive functional equation:‎ ‎$$sum_{i=1}^m f(x_i)=frac{1}{2m}left[sum_{i=1}^mfle...

in this paper, we classify the indecomposable non-nilpotent solvable lie algebras with $n(r_n,m,r)$ nilradical,by using the derivation algebra and the automorphism group of $n(r_n,m,r)$.we also prove that these solvable lie algebras are complete and unique, up to isomorphism.

Deformed orthogonal and pseudo-orthogonal Lie algebras are constructed which differ from deformations of Lie algebras in terms of Cartan subalgebras and root vectors and which make it possible to construct representations by operators acting according to Gel’fand–Tsetlin-type formulas. Unitary representations of the q-deformed algebras Uq(son,1) are found. AMS subject classifications (1980). 16...

In this paper we study the complete reducibility of representations of infinitedimensional Lie algebras from the perspective of representation theory of vertex algebras.

We construct ternary self-distributive (TSD) objects from compositions of binary Lie algebras, 3-Lie algebras and, in particular, Nambu-Lie algebras. show that the structures obtained satisfy an invertibility property resembling racks. prove these give rise to Yang-Baxter operators tensor product base vector space upon defining suitable twisting isomorphisms, we obtain representations infinite ...