Type II non-commutative geometry. I. Dixmier trace in von Neumann algebras

By M. Benameur, T. Fack. 2006

75 citations recorded by the source corpus.

Abstract We define the notion of Connes–von Neumann spectral triple and consider the associated index problem. We compute the analytic Chern–Connes character of such a generalized spectral triple and prove the corresponding local formula for its Hochschild class. This formula involves the Dixmier trace for II ∞ von Neumann algebras. In the case of foliations, we identify this Dixmier trace with the corresponding measured Wodzicki residue.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0af8a67ac3f62ec53d0cdc63b8639e0d197c13e5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Fedor Sukochev
2. Alan L. Carey
3. A. Rennie
4. R. Nest
5. Sergey Neshveyev
6. David Pask
7. Aidan Sims
8. J. Phillips

In Applied Mathematics

1. Fedor Sukochev
2. A. Rennie
3. Alan L. Carey
4. R. Nest
5. Sergey Neshveyev

In Mathematical Physics

1. Alan L. Carey
2. Fedor Sukochev
3. A. Rennie
4. R. Nest
5. Sergey Neshveyev
6. David Pask
7. D. Potapov
8. Aidan Sims

Citations in the corpus

• Dixmier traces and some applications in non-commutative geometry (2006, methodology): “The main result of [ 10 ] on this topic is a formula for the Dixmier trace of certain pseudodifferential operators in terms of a local residue where the latter is a generalisation of the Wodzicki residue to the foliation setting.”
• The Dixmier trace and asymptotics of zeta functions (2006, unknown): “Our reason for striving for generality stems from the emergence recently of applications of the semifinite von Neumann theory [1, 2 , 18, 4, 5, 35].”
• Twisted cyclic theory, equivariant KK-theory and KMS states (2008, background): “Our main reference for the analytic part of these ideas is [7], however there is more background in [ 4 , 10, 11, 12].”