Gradings on Simple Lie Algebras
- ISBN-10
- 0821898469
- ISBN-13
- 9780821898468
- Category
- Mathematics
- Pages
- 336
- Language
- English
- Published
- 2013
- Publisher
- American Mathematical Soc.
- Authors
- Alberto Elduque, Mikhail Kochetov
Description
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.
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