Lie Groups, Lie Algebras and Representations

Part of the Mathematics: Theory & Applications book series (MTA)


In this preliminary chapter we will outline an introduction to basic structure and representation theory of Lie groups and algebras. For those who are not already acquainted with this material, the hope is that the little we will say, perhaps supplementing a little from the quoted literature, could be enough to proceed without plunging into a long and serious study of the many things involved in this theory. For those who are already familiar with the matter, this chapter can either be skipped, or can serve as a quick reminder of some of the main points. To keep it as simple as possible, we will mostly explain things in the case of matrix groups, which in any case contains the main examples.


Positive Root Simple Root Associative Algebra Verma Module Weyl Chamber 
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© Birkhäuser Boston 2006

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