03660nam 2200589 450 991078889200332120170821170812.01-4704-0355-2(CKB)3360000000464392(EBL)3113471(SSID)ssj0000973483(PQKBManifestationID)11582530(PQKBTitleCode)TC0000973483(PQKBWorkID)10959880(PQKB)11745366(MiAaPQ)EBC3113471(RPAM)1792010(PPN)195410912(EXLCZ)99336000000046439220780628h19781978 uy| 0engur|n|---|||||txtccrExceptional Lie algebras and the structure of hermitian symmetric spaces /Daniel DruckerProvidence, Rhode Island :American Mathematical Society,[1978]©19781 online resource (214 p.)Memoirs of the American Mathematical Society ;volume 16, issue 1, number 208 (September 1978)Cover title.0-8218-2208-X 0-8218-3935-7 Includes bibliographical references.""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 27â€?DIMENSIONAL EXCEPTIONAL DOMAIN""; ""1. Determination of bounded realization by use of Tits' construction""; ""2. Comparison with the realizations of Koecher and Ise""; ""VI. THE 16â€?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""Memoirs of the American Mathematical Society ;number 208.Exceptional Lie algebrasHermitian symmetric spacesExceptional Lie algebras.Hermitian symmetric spaces.512/.55Drucker Daniel1946-1545060MiAaPQMiAaPQMiAaPQBOOK9910788892003321Exceptional Lie algebras and the structure of hermitian symmetric spaces3799711UNINA