Miemietz, Vanessa; Turner, Will

Hochschild Cohomology of Polynomial Representations of $\mathrm{GL}_2$

Doc. Math. 23, 117-170 (2018)
DOI: 10.25537/dm.2018v23.117-170

Summary

We compute the Hochschild cohomology algebras of Ringel-self-dual blocks of polynomial representations of $\mathrm{GL}_2$ over an algebraically closed field of characteristic $p>2$, that is, of any block whose number of simple modules is a power of $p$. These algebras are finite-dimensional and we provide an explicit description of their bases and multiplications.

Mathematics Subject Classification

20G05, 16E45

Keywords/Phrases

Hochschild cohomology, $\mathrm{GL}_2$, Koszul duality, differential graded algebras

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Affiliation

Miemietz, Vanessa
School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, UK
Turner, Will
Department of Mathematics, University of Aberdeen, Fraser Noble Building, King's College, Aberdeen AB24 3UE, UK

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