• Split Malcev Algebras

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/122/02/0181-0187

• # Keywords

Malcev algebras; structure theory; roots; root spaces.

• # Abstract

We study the structure of split Malcev algebras of arbitrary dimension over an algebraically closed field of characteristic zero. We show that any such algebras 𝑀 is of the form $M=\mathcal{U}+\sum_jI_j$ with $\mathcal{U}$ a subspace of the abelian Malcev subalgebra 𝐻 and any $I_j$ a well described ideal of 𝑀 satisfying $[I_j, I_k]=0$ if $j\neq k$. Under certain conditions, the simplicity of 𝑀 is characterized and it is shown that 𝑀 is the direct sum of a semisimple split Lie algebra and a direct sum of simple non-Lie Malcev algebras.

• # Author Affiliations

1. Departamento de Matemáticas, Universidad de Cádiz, 11510 Puerto Real, Cádiz, Spain

• # Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019