A geometric presentation for the adjoint module of \(SL_ 3(k)\)

DOI10.1016/0021-8693(89)90278-0zbMath0688.20021OpenAlexW1987420572MaRDI QIDQ1263672

Stephen D. Smith, 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)90278-0

zbMATH Keywords

adjoint actionprojective plane\(SL_ 3(k)\)-modulegeometry of group representations

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Representation theory for linear algebraic groups (20G05) Simplicial sets and complexes in algebraic topology (55U10) Combinatorial geometries and geometric closure systems (51D20) Cohomology theory for linear algebraic groups (20G10) Other finite nonlinear geometries (51E25)

Related Items (4)

A bound for the dimension of \(H_ 0({\mathcal F}_ V)\) of modules \(V(\lambda_ i+\lambda_ j)\) for \(A_ l(q)\) ⋮ 1-cohomology of Chevalley groups ⋮ On the geometry of the adjoint representation of a Chevalley group ⋮ A geometric presentation of the 26-dimensional module for \(F_ 4(q)\)

Cites Work

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• Sheaves on buildings and modular representations of Chevalley groups
• On the geometry of the adjoint representation of a Chevalley group
• Classical locally finite Tits chamber systems of rank 3
• On the 1-cohomology of the general and special linear groups
• Apartments and the cayley-algebra module for G₂(k)
• The 1-Cohomology of the Adjoint Module of a Chevalley Group
• Computation of 2-modular sheaves and representations forL₄(2)A₇, 3S₆, andM₂₄
• Introduction to Algebraic K-Theory. (AM-72)

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