Real representations of semisimple Lie algebras have Q-forms

2002/05/28 by Dave Witte, Witte, Dave · 1 citation
Mathematics · #17B10 #22E47 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #math.RT #msc:17B10 #msc:22E47

paper · pdf · doi:10.48550/arxiv.math/0205289

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

openalex publication_date 2002/05/28 · arxiv created 2002/12/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• 2-step nilpotent Lie groups arising from semisimple modules

Related

• An explicit rational structure for real semisimple Lie algebras
• On Lusztig's q-analogues of all weight multiplicities of a representation
• Introduction to Representations of Real Semisimple Lie Groups
• Symplectic forms on six dimensional real solvable Lie algebras I
• A remarkable contraction of semisimple Lie algebras