Real representations of semisimple Lie algebras have Q-forms

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.

21 pages, no figures, Latex2e file; added an alternate proof and strengthened the results in the final section, corrected minor errors