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Exceptional Lie Algebras and the Structure of Hermitian Symmetric Spaces.

By: Material type: TextTextSeries: Memoirs of the American Mathematical SocietyPublisher: Providence : American Mathematical Society, 2005Copyright date: ©2005Edition: 1st edDescription: 1 online resource (214 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470403553
Subject(s): Genre/Form: Additional physical formats: Print version:: Exceptional Lie Algebras and the Structure of Hermitian Symmetric SpacesDDC classification:
  • 510/.8 s;512/.55
LOC classification:
  • QA252.3 -- .D78 1978eb
Online resources:
Contents:
Intro -- TABLE OF CONTENTS -- INTRODUCTION -- SOME NOTATIONAL CONVENTIONS -- I. ALGEBRAIC PRELIMINARIES -- 1. Algebras -- 2. Alternative algebras -- 3. Composition algebras -- 4 . Jordan algebras -- 5. The Tits construction -- II. e[sub(6)] AND e[sub(7)] -- 1. Notational conventions -- 2. Some derivation algebras -- 3. The Lie multiplication in e[sub(6)] -- 4. The Lie multiplication in e[sub(7)] -- III. GEOMETRIC PRELIMINARIES -- 1. Adjoint representations -- 2. Cartan decompositions -- 3 . Hermitian symmetric spaces -- 4. Duality -- 5. Rank -- 6 .Classification -- 7. Roots and Cayley transforms -- 8. Imbedding theorems -- 9. Restricted roots -- 10. Langlands' theorem -- 11 . Orbits and holomorphic arc components -- 12. Jordan structure -- IV. THE CLASSICAL DOMAINS -- 1. The method -- 2. Determination of the realizations -- 3. Equivalence with the standard realizations -- V. THE 27-DIMENSIONAL EXCEPTIONAL DOMAIN -- 1. Determination of bounded realization by use of Tits' construction -- 2. Comparison with the realizations of Koecher and Ise -- VI. THE 16-DIMENSIONAL EXCEPTIONAL DOMAIN -- 1. Determination of bounded realization by use of Tits' construction -- 2. Comparison with the realizations of Koecher and Ise -- VII. ORBITS -- 1 . The orbit pullbacks in general -- 2. Determination of the orbit pullbacks -- VIII. HOLOMORPHIC ARC COMPONENTS -- 1. The holomorphic arc component pullbacks in general -- 2. Determination of the holomorphic arc component pullbacks: the classical cases -- 3. Determination of the holomorphic arc component pullbacks: the exceptional cases -- APPENDIX A. CAYLEY ALGEBRAS -- APPENDIX B. DERIVATIONS OF [omitted]E -- APPENDIX C. DERIVATION ALGEBRAS IN TITS' CONSTRUCTION -- LIST OF NOTATIONS -- BIBLIOGRAPHY.
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Intro -- TABLE OF CONTENTS -- INTRODUCTION -- SOME NOTATIONAL CONVENTIONS -- I. ALGEBRAIC PRELIMINARIES -- 1. Algebras -- 2. Alternative algebras -- 3. Composition algebras -- 4 . Jordan algebras -- 5. The Tits construction -- II. e[sub(6)] AND e[sub(7)] -- 1. Notational conventions -- 2. Some derivation algebras -- 3. The Lie multiplication in e[sub(6)] -- 4. The Lie multiplication in e[sub(7)] -- III. GEOMETRIC PRELIMINARIES -- 1. Adjoint representations -- 2. Cartan decompositions -- 3 . Hermitian symmetric spaces -- 4. Duality -- 5. Rank -- 6 .Classification -- 7. Roots and Cayley transforms -- 8. Imbedding theorems -- 9. Restricted roots -- 10. Langlands' theorem -- 11 . Orbits and holomorphic arc components -- 12. Jordan structure -- IV. THE CLASSICAL DOMAINS -- 1. The method -- 2. Determination of the realizations -- 3. Equivalence with the standard realizations -- V. THE 27-DIMENSIONAL EXCEPTIONAL DOMAIN -- 1. Determination of bounded realization by use of Tits' construction -- 2. Comparison with the realizations of Koecher and Ise -- VI. THE 16-DIMENSIONAL EXCEPTIONAL DOMAIN -- 1. Determination of bounded realization by use of Tits' construction -- 2. Comparison with the realizations of Koecher and Ise -- VII. ORBITS -- 1 . The orbit pullbacks in general -- 2. Determination of the orbit pullbacks -- VIII. HOLOMORPHIC ARC COMPONENTS -- 1. The holomorphic arc component pullbacks in general -- 2. Determination of the holomorphic arc component pullbacks: the classical cases -- 3. Determination of the holomorphic arc component pullbacks: the exceptional cases -- APPENDIX A. CAYLEY ALGEBRAS -- APPENDIX B. DERIVATIONS OF [omitted]E -- APPENDIX C. DERIVATION ALGEBRAS IN TITS' CONSTRUCTION -- LIST OF NOTATIONS -- BIBLIOGRAPHY.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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