Journal of Lie Theory 25 (2015), No. 3, 807--813
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 Lyndon-Hochschild-Serre spectral sequence corresponding to the first Frobenius kernel of an algebraic group G and computing the extensions between simple G-modules. We state and discuss a conjecture that E2 = E∞ and provide general conditions for low-dimensional terms on the E2-page to be the same as the corresponding terms on the E∞-page, i.e. its abutment.
Keywords: Reductive algebraic groups, Lyndon-Hochschild-Serre spectral sequence, positive characteristic, cohomology of simple modules.
MSC: 20G10, 20G05, 18G40
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