The second cohomology of simple SL₃-modules

2009/07/27 by David I. Stewart, Stewart, David I.
Mathematics · #20G10 #20G30 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0907.4626

openalex publication_date 2009/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be the simple, simply connected algebraic group SL₃ defined over an algebraically closed field K of characteristic p>0. In this paper, we find H²(G,V) for any irreducible G-module V. When p>7 we also find H²(G(q),V) for any irreducible G(q)-module V for the finite Chevalley groups G(q)=SL(3,q) where q is a power of p.

Related

• The second cohomology of simple SL₂-modules
• On The Cohomology of SL₂ with Coefficients in a Simple Module
• Cohomology of simple modules for \mathfraksl₃(k) in characteristic 3
• Cohomology of SL₂ and related structures
• Cohomology of \fraksl(2) and its applications in prime characteristic