2007/07/26 by Alastair Hamilton, Andrey Lazarev
Mathematics · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Cohomology #Cyclic homology #De Rham cohomology #Equivariant cohomology #Homotopy #Homotopy and Cohomology in Algebraic Topology #Mathematics #Noncommutative algebraic geometry #Noncommutative geometry #Noncommutative quantum field theory #Pure mathematics #math.AG #math.KT #math.QA
paper · pdf · doi:10.2140/agt.2009.9.1503
published as Algebr. Geom. Topol. 9 (2009) 1503-1583 · This 54 pages paper is a substantial revision of the part of math.QA/0410621 dealing with algebraic Hodge decompositions of Hochschild and cyclic cohomology theories. The main addition is the treatment of cohomology theories corresponding to unital infinity-structures
arxiv created 2007/07/26 · openalex publication_date 2009/08/01 · arxiv updated 2014/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
This paper builds a general framework in which to study cohomology theories of strongly homotopy algebras, namely A 1 -, C 1 -and L 1 -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 1 -algebras. This generalises and puts in a conceptual framework previous work by Loday and Gerstenhaber-Schack.