Real representations of semisimple Lie algebras have Q-forms
Representation Theory
2007-05-23 v3
Abstract
We prove that each real semisimple Lie algebra G has a Q-form, such that every real representation of G can be realized over the rational numbers Q. This was previously proved by M.S.Raghunathan (and rediscovered by P.Eberlein) in the special case where G is compact.
Keywords
Cite
@article{arxiv.math/0205289,
title = {Real representations of semisimple Lie algebras have Q-forms},
author = {Dave Witte},
journal= {arXiv preprint arXiv:math/0205289},
year = {2007}
}
Comments
21 pages, no figures, Latex2e file; added an alternate proof and strengthened the results in the final section, corrected minor errors