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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

David I. Stewart
Dept. of Pure Mathematics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, England

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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