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The structure of compact groups : a primer for students, a handbook for the expert /
Dealing with subject matter of compact groups that is frequently cited in fields like algebra, topology, functional analysis, and theoretical physics, this book - now in its third revised and augmented edition - has been conceived with the dual purpose of providing a text book for upper level gradua...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin ; Boston :
Walter de Gruyter,
[2013]
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| Edición: | Third edition. |
| Colección: | De Gruyter studies in mathematics ;
25. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Chapter 1. Basic Topics and Examples; Definitions and Elementary Examples; Actions, Subgroups, Quotient Spaces; Products of Compact Groups; Applications to Abelian Groups; Projective Limits; Totally Disconnected Compact Groups; Some Duality Theory; Postscript; References for this Chapter-Additional Reading; Chapter 2. The Basic Representation Theory of Compact Groups; Some Basic Representation Theory for Compact Groups; The Haar Integral; Consequences of Haar Measure; The Main Theorem on Hilbert Modules for Compact Groups; Postscript; References for this Chapter-Additional Reading
- Part 2: The Structure Theorem of EfinCyclic Modules; Postscript; References for this Chapter-Additional Reading; Chapter 5. Linear Lie Groups; Preliminaries; The Exponential Function and the Logarithm; Differentiating the Exponential Function in a Banach Algebra; Local Groups for the Campbell-Hausdorff Multiplication; Subgroups of A-1 and Linear Lie Groups; Analytic Groups; The Intrinsic Exponential Function of a Linear Lie Group; The Adjoint Representation of a Linear Lie Group; Subalgebras, Ideals, Lie Subgroups, Normal Lie Subgroups; Normalizers, Centralizers, Centers
- The Commutator SubgroupForced Continuity of Morphisms between Lie Groups; Quotients of Linear Lie Groups; The Topological Splitting Theorem for Normal Vector Subgroups; Postscript; References for this Chapter-Additional Reading; Chapter 6. Compact Lie Groups; Compact Lie algebras; The Commutator Subgroup of a Compact Lie Group; The Structure Theorem for Compact Lie Groups; Maximal Tori; The Second Structure Theorem for Connected Compact Lie Groups; Compact Abelian Lie Groups and their Linear Actions; Action of a Maximal Torus on the Lie Algebra; The Weyl Group Revisited
- The Commutator Subgroup of Connected Compact Lie GroupsOn the Automorphism Group of a Compact Lie Group; Covering Groups of Disconnected Compact Lie Groups; Auerbach's Generation Theorem; The Topology of Connected Compact Lie Groups; Postscript; References for this Chapter-Additional Reading; Chapter 7. Duality of Abelian Topological Groups; The Compact Open Topology and Hom-Groups; Local Compactness and Duality of Abelian Topological Groups; Basic Functorial Aspects of Duality; The Annihilator Mechanism; Character Groups of Topological Vector Spaces; The Exponential Function