Real representations of semisimple Lie algebras have Q-forms

Details Real representations of semisimple Lie algebras have Q-forms Real representations of semisimple Lie algebras have Q-forms

2002-05-28

arxiv.org/abs/math/0205289v3

Mathematics

Representation Theory

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

Scientific paper

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.

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