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Lie Groups, Physics, and Geometry by Robert Gilmore

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9

Structure theory for simple Lie algebras

 

 

In this chapter we continue the development begun in the previous chapter. These two chapters focus on determining the structure of a Lie algebra and putting it into some canonical form. In the previous chapter we determined the types of subalgebras that every Lie algebra is constructed from. In this chapter we put the commutation relations into a standard form. This can be done for any Lie algebra. For semisimple Lie algebras this standard form has a very rigid structure whose usefulness is surpassed only by its beauty.

9.1 Objectives of this program

In the previous chapter we studied the commutation relations of a Lie algebra through its regular representation. This study was carried out using ...

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