Hostname: page-component-7c8c6479df-8mjnm Total loading time: 0 Render date: 2024-03-29T10:15:33.541Z Has data issue: false hasContentIssue false

On Kontsevich's Hochschild cohomology conjecture

Published online by Cambridge University Press:  13 January 2006

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, USAikriz@umich.edu
Alexander A. Voronov
Affiliation:
Department of Mathematics, University of Minnesota, 127 Vincent, 206 Church Street SE, Minneapolis, MN 55455-0487, USA
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Copyright
Foundation Compositio Mathematica 2006