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A Cohomological Proof that Real Representations of Semisimple Lie Algebras Have Q-Forms
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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A Cohomological Proof that Real Representations of Semisimple Lie Algebras Have Q-Forms
Інший ID:
2010 Mathematics Subject Classification: 17B10; 17B20; 11E72; 20G30
DOI:10.3842/SIGMA.2015.034
DOI:10.3842/SIGMA.2015.034
Посилання:
A Cohomological Proof that Real Representations of Semisimple Lie Algebras Have Q-Forms / D.W. Morris // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 12 назв. — англ.
Підтримка:
It is a pleasure to thank V. Chernousov for a very helpful discussion about Tits algebras of special
orthogonal groups, A. Rapinchuk for explaining how to prove Lemma 2.5, and the anonymous
referees for numerous very insightful comments on a previous version of this manuscript, including
some important corrections.
Дата:
2015
Переглядів:
638
Завантажень:
240
Анотація:
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.
