Exceptional Lie algebras and the structure of hermitian symmetric spaces / Daniel Drucker.

Format:

Book

Author/Creator:

Drucker, Daniel, 1946- author.

Series:

Memoirs of the American Mathematical Society ; number 208.

Memoirs of the American Mathematical Society ; volume 16, issue 1, number 208 (September 1978)

Language:

English

Subjects (All):

Exceptional Lie algebras.

Hermitian symmetric spaces.

Physical Description:

1 online resource (214 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [1978]

Language Note:

English

Contents:

""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""

Notes:

Cover title.

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0355-2