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

Vanessa Miemietz; Will Turner

doi:10.4171/dm/615

JournalsdmVol. 23pp. 117–170

Hochschild Cohomology of Polynomial Representations of $GL_{2}$

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

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

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Abstract

We compute the Hochschild cohomology algebras of Ringel-self-dual blocks of polynomial representations of $GL_{2}$ 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.

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Vanessa Miemietz, Will Turner, Hochschild Cohomology of Polynomial Representations of $GL_{2}$ . Doc. Math. 23 (2018), pp. 117–170

DOI 10.4171/DM/615