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Lectures on Real Semisimple Lie Algebras and Their Representations (ESI Lectures in Mathematics & Physics)

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Author(s): Arkady L. Onishchik
Publisher: European Mathematical Society
Year: 2003

Language: English
Pages: 96

Contents......Page 5
Introduction......Page 7
Lie groups and Lie algebras......Page 11
Structure of complex semisimple Lie algebras......Page 14
Representations of Lie algebras......Page 18
§2. Complexification and real forms......Page 22
§3. Real forms and involutive automorphisms......Page 30
§4. Automorphisms of complex semisimple Lie algebras......Page 37
§5. Cartan decompositions and maximal compact subgroups......Page 46
§6. Homomorphisms and involutions of complex semisimple Lie algebras......Page 54
§7. Inclusions between real forms under an irreducible representation......Page 60
§8. Real representations of real semisimple Lie algebras......Page 74
§9. Appendix on Satake diagrams......Page 83
Table 2......Page 87
Table 4......Page 88
Table 5......Page 89
References......Page 93