On Kontsevich's Hochschild cohomology conjecture

Po Hu, Igor Kriz, Alexander A. Voronov

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Generalizing a conjecture of Deligne, Kontsevich proposed that there should be a notion of Hochschild cohomology of algebras over the little cube operad (or its chain complex) which in a natural way generalizes Hochschild cohomology of associative algebras. He moreover conjectured that the Hochschild cohomology, in this new sense, of an algebra over the little k-cube operad is an algebra over the little (k + 1)-cube operad. In this paper, we precisely state and prove this conjecture.

Original languageEnglish (US)
Pages (from-to)143-168
Number of pages26
JournalCompositio Mathematica
Issue number1
StatePublished - 2006


  • Algebraic structures
  • Hochschild cohomology
  • Operads


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