Lie groups and subsemigroups with surjective exponential fuction / / Karl H. Hofmann, Wolfgang A.F. Ruppert

• Record Nr.: UNINA9910788733103321
• Autore: Hofmann Karl Heinrich
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , [1997]; ©1997
• ISBN: 1-4704-0207-6
• Descrizione fisica: 1 online resource (189 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 618
• Disciplina: 510 s; 512/.55
• Soggetti: Lie groups; Loops (Group theory); Topological semigroups
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "November 1997, volume 130, number 618 (second of 4 numbers)."
• Nota di bibliografia: Includes bibliographical references (pages 169-172) and index.
• Nota di contenuto: ""Contents""; ""Chapter 1. Introduction""; ""1. The Problem and its Background""; ""2. A Survey of Methods and Techniques""; ""3. The Major Results""; ""4. Suggestions for the Reader""; ""Chapter 2. The Basic Theory of Exponential Semigroups in Lie Groups""; ""1. Basic Definitions and Examples""; ""2. The Exponential Function and Divisibility""; ""3. The Exponential Image of Lie Wedges and Regularity""; ""4. Maximal Rank Subgroups""; ""5. Interior Points in the Tangent Wedge""; ""Chapter 3. Weyl Groups and Finiteness Properties of Cartan Subalgebras""; ""1. Cartan Dense Ideals""; ""2. Algebraic Hulls""""3. Generalized Weyl Groups""; ""4. Intersections of Cartan Subalgebras""; ""5. Porcupine Varieties""; ""6. Porcupine Varieties are Proper""; ""7. The Codimension of Porcupine Varieties""; ""Chapter 4. Lie Semialgebras""; ""1. Semialgebras Revisited""; ""2. Dispersion of Weakly Exponential Semigroups""; ""3. More about Subtangent Vectors""; ""4. Reductions by Factoring Normal Subgroups""; ""5. Porcupine Varieties and Lie Semialgebras""; ""6. Groups with a Unique Maximal Compact Subgroup""; ""7. More about Lean Sets""; ""Chapter 5. More Examples""; ""1. Examples Connected with the Special Linear Group""""2. Some Results on Injective Images of Lie Subsemigroups""; ""3. Examples Connected with the Motion Algebra""; ""4. Examples Connected with the Oscillator Group""; ""5. Examples Connected with Compact Lie Algebras""; ""Chapter 6. Test Algebras and Groups""; ""1. Extensions of the Motion Algebra and of the Oscillator Algebra""; ""2. Test Objects""; ""3. Locally Direct Products of Lie Groups""; ""4. The Proof of the Testing Theorem""; ""Chapter 7. Groups Supporting Reduced Weakly Exponential Semigroups""; ""1. 'Occam's Razor' and Reduced Weakly Exponential Subsemigroups""""2. The Spectrum of adw is Contained in R U iR""; ""3. Root Spaces with Respect to Real-Valued Roots""; ""4. Weakly Exponential Subsemigroups and Eggert Algebras""; ""Chapter 8. Roots and Root Spaces""; ""1. Roots and Root Spaces""; ""2. The Answer""; ""Chapter 9. Appendix: The Hyperspace of a Locally Compact Space""; ""1. Continuous Lattices, Lawson Topology, and Hyperspaces""; ""2. Continuous Functions""; ""3. The Use of Nets""; ""4. Applications to Topological Algebras""; ""References""; ""Index""; ""A""; ""B""; ""C""; ""D""""E""; ""F""; ""G""; ""H""; ""I""; ""L""; ""M""; ""N""; ""O""; ""P""; ""R""; ""S""; ""T""; ""U""; ""V""; ""W""; ""Z""