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Exceptional Lie algebras and the structure of hermitian symmetric spaces / / Daniel Drucker
| Exceptional Lie algebras and the structure of hermitian symmetric spaces / / Daniel Drucker |
| Autore | Drucker Daniel <1946-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [1978] |
| Descrizione fisica | 1 online resource (214 p.) |
| Disciplina | 512/.55 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Exceptional Lie algebras
Hermitian symmetric spaces |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0355-2 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""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"" |
| Record Nr. | UNINA-9910479916003321 |
Drucker Daniel <1946->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [1978] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Exceptional Lie algebras and the structure of hermitian symmetric spaces / / Daniel Drucker
| Exceptional Lie algebras and the structure of hermitian symmetric spaces / / Daniel Drucker |
| Autore | Drucker Daniel <1946-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [1978] |
| Descrizione fisica | 1 online resource (214 p.) |
| Disciplina | 512/.55 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Exceptional Lie algebras
Hermitian symmetric spaces |
| ISBN | 1-4704-0355-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""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"" |
| Record Nr. | UNINA-9910788892003321 |
|
Drucker Daniel <1946->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [1978] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Exceptional Lie algebras and the structure of hermitian symmetric spaces / / Daniel Drucker
| Exceptional Lie algebras and the structure of hermitian symmetric spaces / / Daniel Drucker |
| Autore | Drucker Daniel <1946-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [1978] |
| Descrizione fisica | 1 online resource (214 p.) |
| Disciplina | 512/.55 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Exceptional Lie algebras
Hermitian symmetric spaces |
| ISBN | 1-4704-0355-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""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"" |
| Record Nr. | UNINA-9910828122403321 |
|
Drucker Daniel <1946->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [1978] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Maximal Textrm {PSL}_2 Subgroups of Exceptional Groups of Lie Type
| Maximal Textrm {PSL}_2 Subgroups of Exceptional Groups of Lie Type |
| Autore | Craven David A |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Providence : , : American Mathematical Society, , 2022 |
| Descrizione fisica | 1 online resource (168 pages) |
| Disciplina |
512/.482
512.482 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Lie groups
Maximal subgroups Exceptional Lie algebras Group theory and generalizations -- Abstract finite groups -- Simple groups: alternating groups and groups of Lie type Group theory and generalizations -- Linear algebraic groups and related topics -- Exceptional groups |
| ISBN |
9781470470210
9781470451196 |
| Classificazione | 20D0620G41 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Notation and Preliminaries -- Chapter 3. Maximal Subgroups -- Chapter 4. Maximal Subgroups and Subspace Stabilizers -- Chapter 5. Blueprint Theorems for Semisimple Elements -- 5.1. Preliminary Results -- 5.2. Determination of the Bounds for the Minimal Module -- 5.3. Consequences for Maximal Subgroups -- Chapter 6. Unipotent and Semisimple Elements -- 6.1. Actions of Unipotent Elements -- 6.2. Blueprints and Element Orders -- 6.3. Blueprints inside Subgroups of Type ₁ -- 6.4. Traces of Modules for \PGL₂ -- 6.5. The Graph Automorphism of ₄ -- 6.6. Rank-1 Subalgebras of the Lie Algebra -- Chapter 7. Modules for \SL₂ -- 7.1. Modules for \SL₂(2^{ }) -- 7.2. Modules for \SL₂(3^{ }) -- 7.3. Modules for \SL₂( ) -- 7.4. Modules for \SL₂( ^{ }) for ≥5 and > -- 1 -- Chapter 8. Some \PSL₂s inside ₆ in Characteristic 3 -- Chapter 9. Proof of the Theorems: Strategy -- Chapter 10. The Proof for ₄ -- 10.1. Characteristic 2 -- 10.2. Characteristic 3 -- 10.3. Characteristic At Least 5 -- Chapter 11. The Proof for ₆ -- 11.1. Characteristic 2 -- 11.2. Characteristic 3 -- 11.3. Characteristic At Least 5 -- Chapter 12. The Proof for ₇ in Characteristic 2 -- Chapter 13. The Proof for ₇ in Odd Characteristic: \PSL₂ Embedding -- 13.1. Characteristic 3 -- 13.2. Characteristic At Least 5 -- Chapter 14. The Proof for ₇ in Odd Characteristic: \SL₂ Embedding -- 14.1. Characteristic 3 -- 14.2. Characteristic At Least 5 -- Appendix A. Actions of Maximal Positive-Dimensional Subgroups on Minimal and Adjoint Modules -- Appendix B. Traces of Small-Order Semisimple Elements -- Bibliography -- Back Cover. |
| Record Nr. | UNINA-9910957558303321 |
|
Craven David A
|
||
| Providence : , : American Mathematical Society, , 2022 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Soggetto topico
-
Exceptional Lie algebras
(4)
- Hermitian symmetric spaces (3)
- Group theory and generalizations -- Abstract finite groups -- Simple groups: alternating groups and groups of Lie type (1)
- Group theory and generalizations -- Linear algebraic groups and related topics -- Exceptional groups (1)
- Lie groups (1)