0000000000814607

AUTHOR

Alain Connes

showing 2 related works from this author

Hopf algebras, renormalization and noncommutative geometry

1998

We explore the relation between the Hopf algebra associated to the renormalization of QFT and the Hopf algebra associated to the NCG computations of transverse index theory for foliations.

High Energy Physics - TheoryPhysicsMathematics::Rings and AlgebrasMathematics - Operator AlgebrasFOS: Physical sciencesStatistical and Nonlinear PhysicsHopf algebraNoncommutative geometryRenormalizationHigh Energy Physics - Theory (hep-th)Mathematics::Quantum AlgebraMathematics - Quantum AlgebraFOS: MathematicsQuantum Algebra (math.QA)Operator Algebras (math.OA)Mathematical PhysicsMathematical physics
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Closed star products and cyclic cohomology

1992

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 t…

Pure mathematicsStatistical and Nonlinear PhysicsMathematics::Algebraic TopologyCohomologyAlgebraMathematics::K-Theory and HomologyCup productDe Rham cohomologyCotangent bundleEquivariant cohomologyTodd classMathematics::Symplectic GeometryMathematical PhysicsSymplectic manifoldQuantum cohomologyMathematicsLetters in Mathematical Physics
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