Abstract
In this note we give a new existence proof for the universal extension classes for G L 2 previously constructed by Friedlander and Suslin via the theory of strict polynomial functors. The key tool in our approach is a calculation of Parker showing that, for suitable choices of coefficient modules, the Lyndon–Hochschild–Serre spectral sequence for S L 2 relative to its first Frobenius kernel stabilizes at the E 2-page. Consequently, we obtain a new proof that if G is an infinitesimal subgroup scheme of G L 2, then the cohomology ring H∙(G,k) of G is a finitely-generated noetherian k-algebra.
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Drupieski, C.M. Universal Extension Classes for GL 2 . Algebr Represent Theor 17, 1853–1860 (2014). https://doi.org/10.1007/s10468-014-9475-x
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DOI: https://doi.org/10.1007/s10468-014-9475-x