Gradings on simple Lie algebras
QA3 .A4 V.189
- Unknown QA3 .A4 V.189
- Kochetov, Mikhail, 1977-
- Includes bibliographical references (p. 323-329) and indexes.
- Introduction Gradings on algebras Associative algebras Classical Lie algebras Composition algebras and type $G_2$ Jordan algebras and type $F_4$ 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.
- (source: Nielsen Book Data)
- Publisher's 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 neighbouring areas. This book is published in cooperation with Atlantic Association for Research in the Mathematical Sciences (AARMS).
(source: Nielsen Book Data)
- Lie algebras.
- Rings (Algebra)
- Jordan algebras.
- Nonassociative rings and algebras > Lie algebras and Lie superalgebras > Graded Lie (super)algebras.
- Nonassociative rings and algebras > Lie algebras and Lie superalgebras > Lie (super)algebras associated with other structures (associative, Jordan, etc.)
- Associative rings and algebras > Rings and algebras with additional structure > Graded rings and modules.
- Nonassociative rings and algebras > General nonassociative rings > Composition algebras.
- Nonassociative rings and algebras > Jordan algebras (algebras, triples and pairs) > Jordan structures associated with other structures.
- Publication date
- Alberto Elduque, Mikhail Kochetov.
- Mathematical surveys and monographs ; v. 189