Hochschild cohomology of GL2

Vanessa Miemietz, William Brunt Turner

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We compute the Hochschild cohomology algebras of Ringel-self-dual blocks of polynomial representations of GL2 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.
Original languageEnglish
Number of pages36
JournalDocumenta Mathematica
Publication statusPublished - 31 Dec 2018


  • Hochschild cohomology
  • GL2
  • Koszul duality
  • differential graded algebras


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