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In this chapter, we will examine in more detail the representations of simple Lie algebras introduced in Sect. 13.3 and characterize all irreducible representations. In Chap. 14 , we saw that every representation D of a Lie group G induces a representation \(\mathfrak {D}\) of its Lie algebra \(T_eG\) , and the reverse is achieved through the exponential mapping.

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Representations of Lie Algebras

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  • 发表日期：

    2026年

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  • Andreas Wipf

摘要

In this chapter, we will examine in more detail the representations of simple Lie algebras introduced in Sect. 13.3 and characterize all irreducible representations. In Chap. 14 , we saw that every representation D of a Lie group G induces a representation \(\mathfrak {D}\) of its Lie algebra \(T_eG\) , and the reverse is achieved through the exponential mapping.