Ela Postlie Algebra Structures on the Lie Algebra Sl(2,c)∗

PostLie algebra structures on the Lie Algebra SL(2,Ca)

Modules of the toroidal Lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$

‎Highest weight modules of the double affine Lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$ are studied under a‎ ‎new triangular decomposition‎. ‎Singular vectors of Verma modules are‎ ‎determined using a similar condition with horizontal affine Lie‎ ‎subalgebras‎, ‎and highest weight modules are described under the‎ ‎condition $c_1>0$ and $c_2=0$.

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...

The Simple Non-lie Malcev Algebra as a Lie-yamaguti Algebra

The simple 7-dimensional Malcev algebra M is isomorphic to the irreducible sl(2,C)-module V (6) with binary product [x, y] = α(x ∧ y) defined by the sl(2,C)-module morphism α : Λ2V (6)→ V (6). Combining this with the ternary product (x, y, z) = β(x∧y) ·z defined by the sl(2,C)-module morphism β : Λ2V (6)→ V (2) ≈ sl(2,C) gives M the structure of a generalized Lie triple system, or Lie-Yamaguti ...

Invariant Nonassociative Algebra Structures on Irreducible Representations of Simple Lie Algebras

An irreducible representation of a simple Lie algebra can be a direct summand of its own tensor square. In this case, the representation admits a nonassociative algebra structure which is invariant in the sense that the Lie algebra acts as derivations. We study this situation for the Lie algebra sl(2).