Gradings on simple Lie algebras
 Author/Creator
 Elduque, Alberto.
 Language
 English.
 Publication
 Providence, Rhode Island : American Mathematical Society, 2013.
 Physical description
 xiii, 336 pages : ill. ; 26 cm.
 Series
 Mathematical surveys and monographs ; v. 189.
Access
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QA3 .A4 V.189
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Contributors
 Contributor
 Kochetov, Mikhail, 1977
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 323329) and indexes.
 Contents

 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 thirtyone Cartan subalgebras. This monograph is a selfcontained 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)
Subjects
 Subject
 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.
Bibliographic information
 Publication date
 2013
 Responsibility
 Alberto Elduque, Mikhail Kochetov.
 Series
 Mathematical surveys and monographs ; v. 189
 ISBN
 9780821898468 (alk. paper)
 0821898469 (alk. paper)