6. 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
Keywords: Hochschild cohomology, $GL_2$, Koszul duality, differential graded algebras


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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