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Maximal finite abelian subgroups of E8

Part of: Linear algebraic groups and related topics Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  29 June 2017

Cristina Draper  and
Alberto Elduque
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)
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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.

Keywords

maximal finite abelian subgroupsfine gradingsE8

MSC classification

Secondary: 17B25: Exceptional (super)algebras 17B40: Automorphisms, derivations, other operators 20G15: Linear algebraic groups over arbitrary fields
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 147 , Issue 5 , October 2017 , pp. 993 - 1008
Copyright
Copyright © Royal Society of Edinburgh 2017