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Representations of Lie Algebras by Anthony Henderson

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CHAPTER 6

General theory of modules

In this chapter we return to the theory of modules over an arbitrary Lie algebra Image. There is a great deal that could be said, even in this generality, but we will concentrate on the concepts needed for our study of integral Image-modules in the next chapter.

6.1 Duals and tensor products

A feature that the theory of modules over Lie algebras shares with the representation theory of groups is that there is a natural operation of duality. Recall that, for any vector space V, the dual space V* consists of all the linear ...

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