1-cohomology of Chevalley groups

DOI10.1016/0021-8693(89)90257-3zbMath0687.20039OpenAlexW2013034711MaRDI QIDQ1262953

Helmut Voelklein

Publication date: 1989

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(89)90257-3

zbMATH Keywords

extensionssimple moduleshighest weightChevalley groupBorel subgroup

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Representation theory for linear algebraic groups (20G05) Cohomology theory for linear algebraic groups (20G10)

Related Items (3)

On Medium-Rank Lie Primitive and Maximal Subgroups of Exceptional Groups of Lie Type ⋮ A bound for the dimension of \(H_ 0({\mathcal F}_ V)\) of modules \(V(\lambda_ i+\lambda_ j)\) for \(A_ l(q)\) ⋮ A geometric presentation of the 26-dimensional module for \(F_ 4(q)\)

Cites Work

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• Extensions of simple modules for finite Chevalley groups
• Die adjungierten Darstellungen der Chevalley-Gruppen
• Universal presheaves on group geometries, and modular representations
• Sheaves on buildings and modular representations of Chevalley groups
• Sheaf homology and complete reducibility
• Centers of Chevalley algebras
• Irreducible modules and parabolic subgroups
• Rational and generic cohomology
• Cohomology of finite groups of Lie type. I
• A geometric presentation for the adjoint module of \(SL_ 3(k)\)
• On the geometry of the adjoint representation of a Chevalley group
• Duality for presheaves on chamber systems, and a related chain complex
• Irreducible modular representations of finite Chevalley groups
• The 1-Cohomology of the Adjoint Module of a Chevalley Group
• The Projective Indecomposable Modules of SL(2, p ⁿ )
• Cohomology of certain Steinberg groups

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