Split Malcev Algebras

Proceedings Mathematical Sciences

Manuel Forero Piulestán¹  Antonio J Calderón Martín²  José M Sánchez Delgado¹ 

[1] $$;Departamento de Matemáticas, Universidad de Cádiz, 0 Puerto Real, Cádiz, Spain$$

关键词: Malcev algebras;    structure theory;    roots;    root spaces.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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 ≠ 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.

【 授权许可】

Unknown