Cohomology theories for homotopy algebras and noncommutative geometry

Alastair Hamilton, Andrey Lazarev

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

This paper builds a general framework in which to study cohomology theories of strongly homotopy algebras, namely A∞-, C∞- a n d L∞-algebras. This framework is based on noncommutative geometry as expounded by Connes and Kontsevich. The developed machinery is then used to establish a general form of Hodge decomposition of Hochschild and cyclic cohomology of C∞-algebras. This generalises and puts in a conceptual framework previous work by Loday and Gerstenhaber -Schack.

Original languageEnglish
Pages (from-to)1503-1583
Number of pages81
JournalAlgebraic and Geometric Topology
Volume9
Issue number3
DOIs
StatePublished - 2009

Keywords

  • Cyclic cohomology
  • Harrison cohomology
  • Hodge decomposition
  • Infinityalgebra
  • Symplectic structure

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