caa a22 4500 469099062 CHVBK 20180323133040.0 cr unu---uuuuu 170328e19920101xx s 000 0 eng 10.1007/BF00429997 doi (NATIONALLICENCE)springer-10.1007/BF00429997 Closed star products and cyclic cohomology [Elektronische Daten] [Alain Connes, Moshé Flato, Daniel Sternheimer] We define the notion of a closed star product. A (generalized) star product (deformation of the associative product of functions on a symplectic manifold W) is closed iff integration over W is a trace on the deformed algebra. We show that for these products the cyclic cohomology replaces the Hochschild cohomology in usual star products. We then define the character of a closed star product as the cohomology class (in the cyclic bicomplex) of a well-defined cocycle, and show that, in the case of pseudodifferential operators (standard ordering on the cotangent bundle to a compact Riemannian manifold), the character is defined and given by the Todd class, while in general it fails to satisfy the integrality condition. Kluwer Academic Publishers, 1992 Connes Alain Collège de France, 3 rue d'Ulm, F-75005, Paris, France aut Flato Moshé Physique Mathématique, Faculté des Sciences Mirande, Université de Bourgogne, BP 138, F-21004, Dijon Cedex, France aut Sternheimer Daniel Physique Mathématique, Faculté des Sciences Mirande, Université de Bourgogne, BP 138, F-21004, Dijon Cedex, France aut Letters in Mathematical Physics Kluwer Academic Publishers 24/1(1992-01-01), 1-12 0377-9017 24:1<1 1992 24 11005 https://doi.org/10.1007/BF00429997 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00429997 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Connes Alain Collège de France, 3 rue d'Ulm, F-75005, Paris, France aut NATIONALLICENCE 700 1- Flato Moshé Physique Mathématique, Faculté des Sciences Mirande, Université de Bourgogne, BP 138, F-21004, Dijon Cedex, France aut NATIONALLICENCE 700 1- Sternheimer Daniel Physique Mathématique, Faculté des Sciences Mirande, Université de Bourgogne, BP 138, F-21004, Dijon Cedex, France aut NATIONALLICENCE 773 0- Letters in Mathematical Physics Kluwer Academic Publishers 24/1(1992-01-01), 1-12 0377-9017 24:1<1 1992 24 11005 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer