A Cohomological Proof that Real Representations of Semisimple Lie Algebras Have Q-Forms

作者：Morris Dave Witte^*

来源：Symmetry Integrability and Geometry-Methods and Applications, 2015, 11: 034.

DOI：10.3842/SIGMA.2015.034

• semisimple Lie algebra
• finite-dimensional representation
• global field
• Galois cohomology
• linear algebraic group
• Tits algebra

A Lie algebra gQ over Q is said to be I universal if every homomorphism from gQ to gl(n, R) is conjugate to a homomorphism into gi(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 N-universal Q-form. We also provide a classification of the I universal Lie algebras that are semisimple.

• 出版日期2015