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Maximal finite abelian subgroups of E8

Published online by Cambridge University Press:  29 June 2017

Cristina Draper
Affiliation:
Departamento de Matemática Aplicada, Escuela de las Ingenierías, Universidad de Málaga, Ampliación Campus de Teatinos, 29071 Málaga, Spain (cdf@uma.es)
Alberto Elduque
Affiliation:
Departamento de Matemáticas e Instituto Universitario de Matemáticas y Aplicaciones, Universidad de Zaragoza, 50009 Zaragoza, Spain (elduque@unizar.es)

Extract

The maximal finite abelian subgroups, up to conjugation, of the simple algebraic group of type E8 over an algebraically closed field of characteristic 0 are computed. This is equivalent to the determination of the fine gradings on the simple Lie algebra of type E8 with trivial neutral homogeneous component. The Brauer invariant of the irreducible modules for graded semisimple Lie algebras plays a key role.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2017 

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