UID:
edocfu_9958104327302883
Format:
1 online resource (257 p.)
ISBN:
1-281-76337-3
,
9786611763374
,
0-08-087322-7
Series Statement:
Pure and applied mathematics, a series of monographs and textbooks ; 10-V
Content:
Spectral Theory of Random Matrices
Note:
Description based upon print version of record.
,
Front Cover; Treatise on Analysis; Copyright Page; Contents; Notation; Chapter XXI. COMPACT LIE GROUPS AND SEMISIMPLE LIE GROUPS; I . Continuous unitary representations of locally compact groups; 2. The Hilbert Algebra of a compact group; 3. Characters of a compact group; 4. Continuous unitary representations of compact groups; 5. Invariant bilinear forms; the Killing form; 6. Semisimple Lie groups. Criterion of semisimplicity for a compact Lie group; 7. Maximal tori in compact connected Lie groups; 8. Roots and almost simple subgroups of rank; 9. Linear representations of SU(2)
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10. Properties of the roots of a compact semisimple group11. Bases of a root system; 12. Examples: the classical compact groups; 13. Linear representations of compact connected Lie groups; 14. Anti-invariant elements; 15. Weyl's formulas; 16. Center, fundamental group and irreducible representations of semisimple compact connected groups; 17. Complexifications of compact connected semisimple groups; 18. Real forms of the complexifications of compact connected semisimple groups and symmetric spaces; 19. Roots of a complex semisimple Lie algebra; 20. Weyl bases; 21. The Iwasawa decomposition
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22. Cartan's criterion for solvable Lie algebras23. E. E. Levi's theorem; Appendix; 22. Simple modules; 23. Semisimple modules; 24. Examples; 25. The canonical decomposition of an endomorphism; 26. Finitely generated Z-modules; References; Index
,
English
Additional Edition:
ISBN 0-12-215505-X
Language:
English
