Lie Groups And Lie Algebras

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Lie Groups And Lie Algebras 
Robert Glimore


Table of Contents 

1  Tangent Lie algebras to Lie groups

2  Simply Connected Lie Groups

3  The universal enveloping algebra

4  Universality of Ug

5  The PBW Theorem and Deformations

6  Lie algebra cohomology

7  Engel’s Theorem and Lie’s Theorem

8  Cartan Criterion, Whitehead and Weyl Theorems

9  The root system of a semisimple Lie algebra

10 Dynkin diagrams, Classification of root systems

11 Serre’s Theorem

12 Constructions of Exceptional simple Lie Algebras

13 Representations of Lie algebras

14 The Weyl character formula

15 Compact Lie groups

16 An overview of Lie groups

17 Clifford algebras

18 Clifford groups, Spin groups, and Pin groups

19 Spin representations of Spin and Pin groups

20 E8

21 Construction of E8

22 Construction of the Lie group of E8

23 Working with simple Lie groups

24 Irreducible unitary representations of SL2 (R)

25 Unitary representations of SL2 (R)



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