Mathematical surveys and monographs· 2013
Gradings on Simple Lie Algebras
- 246citations
- 2013year
Short summary
This monograph provides a self-contained exposition and classification of gradings by arbitrary groups on classical simple Lie algebras, particularly in characteristics other than 2.
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Key points
- Classifies gradings by arbitrary groups on classical simple Lie algebras.
- Covers characteristic not equal to 2, and some positive characteristic cases.
- Includes related algebras: matrix algebras, octonions, Albert algebra.
- Presents recent results not yet published in book form.
AI-generated from the title and abstract; the full text is not read.
Abstract
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.
The authors' abstract, as published at the source. Mathematical surveys and monographs, 2013 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics