ar X iv : 0 70 7 . 39 37 v 1 [ m at h . Q A ] 2 6 Ju l 2 00 7 COHOMOLOGY THEORIES FOR HOMOTOPY ALGEBRAS AND NONCOMMUTATIVE GEOMETRY
نویسندگان
چکیده
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 generalizes and puts in a conceptual framework previous work by Loday and Gerstenhaber-Schack.
منابع مشابه
ar X iv : m at h / 04 10 62 1 v 1 [ m at h . Q A ] 2 9 O ct 2 00 4 HOMOTOPY ALGEBRAS AND NONCOMMUTATIVE GEOMETRY
We study cohomology theories of strongly homotopy algebras, namely A∞, C∞ and L∞-algebras and establish the Hodge decomposition of Hochschild and cyclic cohomology of C∞-algebras thus generalising previous work by Loday and Gerstenhaber-Schack. These results are then used to show that a C∞-algebra with an invariant inner product on its cohomology can be uniquely extended to a symplectic C∞-alge...
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