Gradings on Simple Lie Algebras
Alberto Elduque · Mikhail Kochetov
Jan 2013 · Mathematical Surveys and Monographs Ibhuku elingu-189 · American Mathematical Soc.
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336
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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).
This book is published in cooperation with Atlantic Association for Research in the Mathematical Sciences (AARMS).
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