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Gradings on simple Lie algebras / Alberto Elduque, Mikhail Kochetov.
- Format:
- Book
- Author/Creator:
- Elduque, Alberto, author.
- Kochetov, Mikhail, 1977- author.
- Series:
- Mathematical surveys and monographs ; Volume 189.
- Mathematical surveys and monographs ; Volume 189
- Language:
- English
- Subjects (All):
- Lie algebras.
- Rings (Algebra).
- Jordan algebras.
- Physical Description:
- 1 online resource (xiii, 336 pages) : illustrations.
- Edition:
- 1st ed.
- Place of Publication:
- Providence, Rhode Island : American Mathematical Society, [2013]
- Language Note:
- English
- Summary:
- Gradings are ubiquitous in the theory of Lie algebras, from the root space decomposition of a complex semisimple Lie algebra relative to a Cartan subalgebra to the beautiful Dempwolff decomposition of E_8 as a direct sum of thirty-one Cartan subalgebras. This monograph is a self-contained exposition of the classification of gradings by arbitrary groups on classical simple Lie algebras over algebraically closed fields of characteristic not equal to 2 as well as on some nonclassical simple Lie algebras in positive characteristic. Other important algebras also enter the stage: matrix algebras, the octonions, and the Albert algebra. Most of the presented results are recent and have not yet appeared in book form. This work can be used as a textbook for graduate students or as a reference for researchers in Lie theory and neighboring areas.
- Contents:
- Cover
- Title page
- Contents
- List of figures
- Preface
- Conventions and dependence among chapters
- Introduction
- Gradings on algebras
- Associative algebras
- Classical Lie algebras
- Composition algebras and type ₂
- Jordan algebras and type ₄
- Other simple Lie algebras in characteristic zero
- Lie algebras of Cartan type in prime characteristic
- Affine group schemes
- Irreducible root systems
- Bibliography
- Index of Notation
- Index
- Back Cover.
- Notes:
- Bibliographic Level Mode of Issuance: Monograph
- Includes bibliographical references (pages 323-329) and indexes.
- Description based on print version record.
- Description based on publisher supplied metadata and other sources.
- ISBN:
- 1-4704-0995-X
- OCLC:
- 898200182
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