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Representations of Lie Algebras by Anthony Henderson

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CHAPTER 5

The theory ofImage-modules

In this chapter we study the representation theory of the smallest simple Lie algebra, Image. The theory as we will develop it goes back to Cartan in the 1890s, but it seems that the results were known to Lie and his student Engel even earlier.

5.1 Classification of irreducibles

Recall from Example 4.1.5 that anImage-module is a vector space V with three linear transformations eV, hV, ƒV that satisfy the bracket relations

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