UID:
almafu_9958115643702883
Umfang:
1 online resource (375 p.)
ISBN:
1-281-98412-4
,
9786611984120
,
0-08-087366-9
Serie:
Pure and applied mathematics; a series of monographs and textbooks ; v. 51
Inhalt:
Introduction to Lie groups and Lie algebras
Anmerkung:
Description based upon print version of record.
,
Front Cover; Introdction to Lie Groups and Lie Algebras; Copyright Page; Contents; Preface; Chapter 1. Some Calculus; 1. Basic Notation; 2. The Derivative; 3. Higher Derivatives; 4. Taylor's Formula; 5. Inverse Function Theorem; 6. The Algebra gl( V ); Chapter 2. Manifolds; 1. Differentiable Structures; 2. Differentiable Functions; 3. Submanifolds; 4. Tangents and Cotangents; 5. Tangent Maps (Differentials); 6. Tangent Bundle; 7. Vector Fields; 8. Integral Curves; Chapter 3. Topological Groups; 1. Basics; 2. Subgroups and Homogeneous Spaces; 3. Connected Groups; Chapter 4. Lie Groups
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1. Basic Structures2. Local Lie Groups; 3. Lie Subgroups; Chapter 5. The Lie Algebra of a Lie Group; 1. The Lie Algebra; 2. The Exponential Map; 3. Exponential Formulas; 4. Homomorphisms and Analytic Structure; Chapter 6. Lie Subgroups and Subalgebras; 1. Lie Subalgebra and Uniqueness of Analytic Structure; 2. Local Isomorphisms; 3. Closed Subgroups; 4. Homogeneous Spaces; 5. Commutative Lie Groups; Chapter 7. Automorphisms and Adjoints; 1. Automorphisms of Algebras; 2. Inner Derivations and Automorphisms; 3. Adjoint Representations; Chapter 8. Simply Connected Lie Groups; 1. Homotopy Review
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2. Simply Connected Covering GroupsChapter 9. Some Algebra; 1. Tensor Products; 2. Extension of the Base Field; 3. Complexification; 4. Modules and Representations; 5. Semisimple Modules; 6. Composition Algebras; Chapter 10. Solvable Lie Groups and Algebras; 1. Solvable Lie Groups; 2. Solvable Lie Algebras and Radicals; 3. Lie's Theorem on Solvability; Chapter 11. Nilpotent Lie Groups and Algebras; 1 . Nilpotent Lie Groups; 2. Nilpotent Lie Algebras; 3. Nilpotent Lie Algebras of Endomorphisms; Chapter 12. Semisimple Lie Groups and Algebras; 1. Invariant Bilinear Forms; 2. Cartan's Criteria
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3. Ideals and Derivations of Semisimple Lie Algebras4. Complete Reducibility and Semisimplicity; 5. More on Radicals, Derivations, and Tensor Products; 6. Remarks on Real Simple Lie Algebras and Compactness; Chapter 13. Cartan Subalgebras and Root Spaces; 1. Cartan Subalgebras; 2. Root Spaces of Split Semisimple Lie Algebras; 3. lrreducible Representations of sl(42,K); Chapter 14. Simple Split Lie Algebras; 1. Root Systems; 2. Classification of Split Simple Lie Algebras; 3. On Automorphisms of Simple Complex Lie Algebras; Chapter 15. Simple Real Lie Algebras and Groups
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1 . Real Forms of Simple Complex Lie Algebra2. Representations of Real and Complex Simple Lie Algebras; 3. Some Simple Real and Complex Lie Groups; Appendix: Some Differential Geometry; 1. Connections on Manifolds; 2. Connections on Homogeneous Spaces and Nonassociative Algebras; 3. Multiplicative Systems and Connections; 4. Riemannian Connections and Jordan Algebras; References; Index; Pure and Applied Mathematics
,
English
Weitere Ausg.:
ISBN 0-12-614550-4
Sprache:
Englisch
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