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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Classifying semisimple orbits of $\theta$-groups
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by Willem A. de Graaf and Francesco Oriente PDF
Math. Comp. 83 (2014), 2509-2526 Request permission


$\theta$-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
  • Email:
  • Francesco Oriente
  • Affiliation: Dipartimento di Matematica, Università di Trento, Italy
  • Email:
  • 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
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 83 (2014), 2509-2526
  • MSC (2010): Primary 17B45, 20G05
  • DOI:
  • MathSciNet review: 3223344