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On Kontsevich's Hochschild cohomology conjecture

Published online by Cambridge University Press:  13 January 2006

Po Hu ,
Igor Kriz  and
Alexander A. Voronov
Po Hu
Affiliation:
Department of Mathematics, Wayne State University, 656 W. Kirby, Rm. 1150 Faculty/Administration Building, Detroit, MI 48202, USA
Igor Kriz
Affiliation:
Department of Mathematics, University of Michigan, 2074 E Hall, 525 E University Avenue, Ann Arbor, MI 48109-1109, [email protected]
Alexander A. Voronov
Affiliation:
Department of Mathematics, University of Minnesota, 127 Vincent, 206 Church Street SE, Minneapolis, MN 55455-0487, USA
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Abstract

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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.

Keywords

operadsHochschild cohomologyalgebraic structures18D5055P4813D03
Type
Research Article
Information
Compositio Mathematica , Volume 142 , Issue 1 , January 2006 , pp. 143 - 168
Copyright
Foundation Compositio Mathematica 2006