Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Cohomology theories for homotopy algebras and noncommutative geometry
AU - Hamilton, Alastair
AU - Lazarev, Andrey
PY - 2009
Y1 - 2009
N2 - This paper builds a general framework in which to study cohomology theories of strongly homotopy algebras, namely A∞–, C∞– and 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.
AB - This paper builds a general framework in which to study cohomology theories of strongly homotopy algebras, namely A∞–, C∞– and 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.
KW - infinity-algebra
KW - cyclic cohomology
KW - Harrison cohomology
KW - symplectic structure
KW - Hodge decomposition
U2 - 10.2140/agt.2009.9.1503
DO - 10.2140/agt.2009.9.1503
M3 - Journal article
VL - 9
SP - 1503
EP - 1583
JO - Algebraic and Geometric Topology
JF - Algebraic and Geometric Topology
SN - 1472-2747
IS - 3
ER -