Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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

 
 

 

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
DOI: https://doi.org/10.1090/S0025-5718-2014-02812-3
Published electronically: February 19, 2014
MathSciNet review: 3223344
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 17B45, 20G05

Retrieve articles in all journals with MSC (2010): 17B45, 20G05


Additional Information

Willem A. de Graaf
Affiliation: Dipartimento di Matematica, Università di Trento, Italy
Email: degraaf@science.unitn.it

Francesco Oriente
Affiliation: Dipartimento di Matematica, Università di Trento, Italy
Email: francesco.oriente@tin.it

DOI: https://doi.org/10.1090/S0025-5718-2014-02812-3
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.

American Mathematical Society