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Representations of sl2, Part I
*July 17, 2009*

*Posted by Akhil Mathew in algebra, representation theory.*

Tags: algebra, Jordan decomposition, Lie algebras, representation theory, semisimplicity, sl2

5 comments

Tags: algebra, Jordan decomposition, Lie algebras, representation theory, semisimplicity, sl2

5 comments

is a special Lie algebra, mentioned in my previous post briefly. It is the set of 2-by-2 matrices over of trace zero, with the Lie bracket defined by:

The representation theory of is important for several reasons.

- It’s elegant.
- It introduces important ideas that generalize to the setting of semisimple Lie algebras.
- Knowing the theory for is useful in the proofs of the general theory, as it is often used as a tool there.

In this way, is an ideal example. Thus, I am posting this partially to help myself learn about Lie algebras.