activity
19982005
most citedFrom Physics to Number Theory via Noncommutative Geometry, Part II: Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory

58 citations · 207 across the 10 of their papers we have counts for

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3 papers · 1 filter

math.OA2005★ 7 cited

KMS states and complex multiplication

Alain Connes, Matilde Marcolli, Niranjan Ramachandran

We construct a quantum statistical mechanical system which generalizes the Bost-Connes system to imaginary quadratic fields K of arbitrary class number and fully incorporates the e…

math.OA2003★ 18 cited

L^2-Homology for von Neumann Algebras

Alain Connes, Dimitri Shlyakhtenko

We define the notion of L^2 homology and L^2 Betti numbers for a tracial von Neumann algebra, or, more generally, for any involutive algebra with a trace. The definition of these i…

math.OA2000

Cyclic Cohomology and Hopf Symmetry

Alain Connes, Henri Moscovici

Cyclic cohomology has been recently adapted to the treatment of Hopf symmetry in noncommutative geometry. The resulting theory of characteristic classes for Hopf algebras and their…