A Cohomological Proof that Real Representations of Semisimple Lie Algebras Have Q-Forms
نویسنده
چکیده
A Lie algebra gQ over Q is said to be R-universal if every homomorphism from gQ to gl(n,R) is conjugate to a homomorphism into gl(n,Q) (for every n). By using Galois cohomology, we provide a short proof of the known fact that every real semisimple Lie algebra has an R-universal Q-form. We also provide a classification of the R-universal Lie algebras that are semisimple.
منابع مشابه
2 8 M ay 2 00 2 REAL REPRESENTATIONS OF SEMISIMPLE LIE ALGEBRAS HAVE Q - FORMS
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