On split Lie algebras with symmetric root systems
 作者： Antonio J. Calderón Martín 作者单位： 1Departamento de Matemáticas, Universidad de Cádiz 刊名： Proceedings Mathematical Sciences, 2008, Vol.118 (3), pp.351-356 来源数据库： Springer Nature Journal DOI： 10.1007/s12044-008-0027-3 关键词： Infinite dimensional Lie algebras;  split Lie algebras;  roots; 英文摘要： Abstract(#br)We develop techniques of connections of roots for split Lie algebras with symmetric root systems. We show that any of such algebras L is of the form L = $$\mathcal{U}$$ + Σ j I j with $$\mathcal{U}$$ a subspace of the abelian Lie algebra H and any I j a well described ideal of L , satisfying [ I j , I k ] = 0 if j ≠ k . Under certain conditions, the simplicity of L is characterized and it is shown that L is the direct sum of the family of its minimal ideals, each one being a simple split Lie algebra with a symmetric root system and having all its nonzero roots connected.

• symmetric　对称的
• split　裂口
• systems　系统科学与软件