
Journal of Lie Theory 25 (2015), No. 3, 807813 Copyright Heldermann Verlag 2015 Stabilisation of the LHS Spectral Sequence for Algebraic Groups Alison E. Parker School of Mathematics, University of Leeds, Leeds LS2 9JT, England a.e.parker@leeds.ac.uk David I. Stewart Dept. of Pure Mathematics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, England dis20@cantab.net We consider the LyndonHochschildSerre spectral sequence corresponding to the first Frobenius kernel of an algebraic group G and computing the extensions between simple Gmodules. We state and discuss a conjecture that E_{2} = E_{∞} and provide general conditions for lowdimensional terms on the E_{2}page to be the same as the corresponding terms on the E_{∞}page, i.e. its abutment. Keywords: Reductive algebraic groups, LyndonHochschildSerre spectral sequence, positive characteristic, cohomology of simple modules. MSC: 20G10, 20G05, 18G40 [ Fulltextpdf (263 KB)] for subscribers only. 