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 algebrassplit Lie algebrasroots
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.
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影响因子:0.191 (2012)

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关键词翻译
关键词翻译
  • symmetric 对称的
  • split 裂口
  • systems 系统科学与软件