We prove a formula for the multiplicity of the irreducible representation V (n) of sl(2, C) as a direct summand of its own exterior cube ΛV (n). From this we determine that V (n) occurs exactly once as a summand of ΛV (n) if and only if n = 3, 5, 6, 7, 8, 10. These representations admit a unique sl(2)-invariant alternating ternary structure obtained from the projection ΛV (n) → V (n). We calcul...

We provide an algorithm for decomposing a finite-dimensional Lie algebra over a field of characteristic 0 permitting to generalize the derivation tower theorem for Lie algebras, is proved by E. Schenkman [4].

Abstract. Xu introduced a class of nongraded Hamiltonian Lie algebras. These Lie algebras have a Poisson bracket structure. In this paper, the isomorphism classes of these Lie algebras are determined by employing a “sandwich” method and by studying some features of these Lie algebras. It is obtained that two Hamiltonian Lie algebras are isomorphic if and only if their corresponding Poisson alge...

In this paper, we consider several different constructions of simple B3-type Lie algebras from several triple systems and the correspondence with extended Dynkin diagrams associated with such triple systems.

Models of the exceptional simple modular Lie superalgebras in characteristic p ≥ 3, that have appeared in the classification due to Bouarroudj, Grozman and Leites [BGLb] of the Lie superalgebras with indecomposable symmetrizable Cartan matrices, are provided. The models relate these exceptional Lie superalgebras to some low dimensional nonassociative algebraic systems. Introduction The finite d...