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Classifying semisimple orbits of $\theta$-groups

Authors: Willem A. de Graaf and Francesco Oriente
Journal: Math. Comp. 83 (2014), 2509-2526
MSC (2010): Primary 17B45, 20G05
Published electronically: February 19, 2014
MathSciNet review: 3223344
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Abstract: $\theta$-groups are a class of reductive algebraic groups arising from $\mathbb {Z}/m\mathbb {Z}$-gradings of simple Lie algebras. They were introduced by Vinberg in the 70s, who developed the theory of their orbits. In this paper we describe algorithms to compute certain objects arising in this theory, namely a Cartan subspace, and the little Weyl group. We have implemented the algorithms in the language of the computer algebra system Magma. Practical experiences with the implementations are discussed.

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Additional Information

Willem A. de Graaf
Affiliation: Dipartimento di Matematica, Università di Trento, Italy
MR Author ID: 610839

Francesco Oriente
Affiliation: Dipartimento di Matematica, Università di Trento, Italy

Received by editor(s): April 8, 2011
Received by editor(s) in revised form: October 14, 2012, and January 6, 2013
Published electronically: February 19, 2014
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.