Exceptional Lie Algebras and the Structure of Hermitian Symmetric Spaces.
Drucker, Daniel.
Exceptional Lie Algebras and the Structure of Hermitian Symmetric Spaces. - 1st ed. - 1 online resource (214 pages) - Memoirs of the American Mathematical Society ; v.16 . - Memoirs of the American Mathematical Society .
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.
9781470403553
Exceptional Lie algebras.
Hermitian symmetric spaces.
Electronic books.
QA252.3 -- .D78 1978eb
510/.8 s;512/.55
Exceptional Lie Algebras and the Structure of Hermitian Symmetric Spaces. - 1st ed. - 1 online resource (214 pages) - Memoirs of the American Mathematical Society ; v.16 . - Memoirs of the American Mathematical Society .
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.
9781470403553
Exceptional Lie algebras.
Hermitian symmetric spaces.
Electronic books.
QA252.3 -- .D78 1978eb
510/.8 s;512/.55