UID:
almafu_9958115646402883
Umfang:
1 online resource (575 p.)
ISBN:
1-281-98218-0
,
9786611982188
,
0-08-087347-2
Serie:
Pure and applied mathematics; a series of monographs and textbooks ; v. 35
Inhalt:
Linear lie groups
Anmerkung:
Description based upon print version of record.
,
Front Cover; Linear Lie Groups, Volume 35; Copyright Page; Contents; 0. Introduction; 0.0 Preface; Chapter 0.1-7. On Notation and Nomenclature; 0.1. Logical Symbols; 0.2. Set Theory Symbols; 0.3. Topological Symbols; 0.4. Algebraic Symbols; 0.5. Analytic Symbols; 0.6. Logograms; 0.7. Nomenclature; Chapter 1-5. Preliminaries; 1. Complex Extension, Real Restriction, and Waiving; 2. The Exponential; 3. Some Lie Groups; 4. Topological Groups; 5 . Differentiable Mappings; Chapter 6-12. The Connection between Local Linear Lie Groups and Lie Algebras
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6. Definition of Local and Global Linear Lie Groups7. The Infinitesimal Algebra of a Local Linear Lie Group; 8. The Exponential Presentation; 9. Homomorphisms, Automorphisms, and Derivations; 10. Expanding Linear Lie Algebras and Their Homomorphisms into Linear Lie Groups and Their Local Homomorphisms; 11. Dropping Differentiability Assumptions; 12. Subgroups and Subalgebras, Normal Subgroups and ldeals; Chapter 13-19. Solvability and Semisimplicity; 13. Solvable Groups and Solvable Lie Algebras; 14. Invariants of Linear Lie Groups and Algebras; 15. Roots and Rank
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16. Important Classes of Complex Lie Algebras17. Solvable Subalgebras; 18. Cleaving; 19. Semisimplicity; Chapter 20-27. Dressings and Classification of Semisimple Complex Lie Algebras; 20. The First Dressing of Complex Semisimple Lie Algebras; 21. The First Weyl Norming and the Second Dressing of Complex Semisimple Lie Algebras; 22. G Determined by W*; 23. The Second Weyl Norming and the Third Dressing of Complex Semisimple Lie Algebras; 24. The Unitary and Standard Restrictions of a Semisimple Lie Algebra; 25. G Determined by W++
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26. Classification of Semisimple Complex Lie Algebras Up to Isomorphism27. G2 and F4. The Chevalley Dressing; Chapter 28-38. Topological and Integration Methods; 28. Homotopy and Wrapping; 29. Fundamental Groups and Wrappings of Topological Groups; 30. Compactness Aspects of Semisimple and Abelian Groups; 31. The Conjugacy Theorem for Centerfree Unitarily Restricted Semisimple Lie Groups; 32. The Fundamental Group of Centerfree Unitarily Restricted Semisimple Groups; 33. The Automorphisms of Semisimple Lie Groups; 34. Integration in Compact Groups; 35. The Conducibility Theorem
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36. Orthogonality Relations37. The Characters of Compact Groups; 38. Some Global Properties of Semisimple Linear Lie Groups; Chapter 39-50. The Algebraic Approach to Linear Representations; 39. The Associative Envelope of a Lie Algebra; 40. The Casimir Tool; 41. Weights and Integral Forms; 42. Source, Top Weight, and Limitation of a Representation; 43. Finite-Dimensional Irreducible Representations; 44. The Construction of All Finite-Dimensional Representations; 45. The Fundamental Weights; 46. The Fundamental Group of Unitarily Restricted Semisimple Lie Groups
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47. Weyl's Character and Dimension Formula
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English
Weitere Ausg.:
ISBN 0-12-374574-8
Sprache:
Englisch
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