Gradings on Simple Lie Algebras
Alberto Elduque, Mikhail Kochetov, "Gradings on Simple Lie Algebras"
English | 2013 | pages: 354 | ISBN: 0821898469 | PDF | 2,6 mb
English | 2013 | pages: 354 | ISBN: 0821898469 | PDF | 2,6 mb
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 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. This book is published in cooperation with Atlantic Association for Research in the Mathematical Sciences (AARMS).
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