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In this chapter, we analyze the commutation relations of semi-simple Lie algebras and their consequences more closely. According to Theorem 13.1 in Sect. 13.4 , every semi-simple Lie algebra is a direct sum of simple ideals, so we only need to consider simple Lie algebras.

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Root Systems and Cartan Classification

  • 章节

  • 发表日期：

    2026年

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  • Andreas Wipf

摘要

In this chapter, we analyze the commutation relations of semi-simple Lie algebras and their consequences more closely. According to Theorem 13.1 in Sect. 13.4 , every semi-simple Lie algebra is a direct sum of simple ideals, so we only need to consider simple Lie algebras.