Third cohomology for Frobenius kernels and related structures

2014/10/09 by Christopher P. Bendel, Bendel, Christopher P., Daniel K. Nakano +3
Mathematics · #17B50 #17B56 #20G05 #20G10 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT #msc:17B50 #msc:17B56 #msc:20G05 #msc:20G10

paper · pdf · doi:10.48550/arxiv.1410.2322

arxiv created 2014/10/09 · arxiv updated 2014/10/10

Abstract

Let G be a simple simply connected group scheme defined over \mathbb F_p and k be an algebraically closed field of characteristic p>0. Moreover, let B be a Borel subgroup of G and U be the unipotent radical of B. In this paper the authors compute the third cohomology group for B and its Frobenius kernels, B_r, with coefficients in a one-dimensional representation. These computations hold with relatively mild restrictions on the characteristic of the field. As a consequence of our calculations, the third ordinary Lie algebra cohomology group for \mathfrak u=Lie U with coefficients in k is determined, as well as the third G_r-cohomology with coefficients in the induced modules H⁰(λ).

Related

• Second cohomology groups for algebraic groups and their Frobenius kernels
• Cohomology of unipotent group schemes
• On nilpotent commuting varieties and cohomology of Frobenius kernels
• On the cohomology of the Ree groups and kernels of exceptional isogenies
• Cohomology of algebraic groups, Lie algebras, and finite groups of Lie type