This paper builds a general framework in which to study cohomology theories of strongly homotopy algebras, namely –, – and –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 –algebras. This generalises and puts in a conceptual framework previous work by Loday and Gerstenhaber–Schack.
"Cohomology theories for homotopy algebras and noncommutative geometry." Algebr. Geom. Topol. 9 (3) 1503 - 1583, 2009. https://doi.org/10.2140/agt.2009.9.1503