The JLO character for the noncommutative space of connections of Aastrup-Grimstrup-Nest

DOI10.1007/s00220-013-1665-6zbMath1261.83025arXiv1010.5226OpenAlexW2964036796MaRDI QIDQ1941084

Alan Lai

Publication date: 11 March 2013

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.5226

zbMATH Keywords

noncommutative spaceconnected compact Lie groupAastrup-Grimstrup-NestAshtekar's loop variablesJLO charactersemi-finite spectral triple

Mathematics Subject Classification ID

Quantization of the gravitational field (83C45) Applications of global analysis to the sciences (58Z05) General properties and structure of complex Lie groups (22E10) Methods of noncommutative geometry in general relativity (83C65) Quantizations, deformations for selfadjoint operator algebras (46L65)

Related Items (6)

Exact traveling wave solutions and bifurcations of the dual Ito equation ⋮ Lifting Bratteli diagrams between Krajewski diagrams: spectral triples, spectral actions, and \textit{AF} algebras ⋮ Spectral action for a one-parameter family of Dirac operators on $\bm{ SU}\textbf {(2)}$SU(2) and $\bm{SU}\textbf {(3)}$SU(3) ⋮ On inductive limit spectral triples ⋮ ON THE JLO COCYCLE AND ITS TRANSGRESSION IN ENTIRE CYCLIC COHOMOLOGY ⋮ QUANTIZATION OF THE G-CONNECTIONS VIA THE TANGENT GROUPOID

Cites Work

• Unnamed Item
• Unnamed Item
• Clifford algebra analogue of the Hopf-Koszul-Samelson theorem, the \(\rho\)-decomposition \(C({\mathfrak g})=\text{End }V_ \rho\otimes C(P)\), and the \({\mathfrak g}\)-module structure of \(\bigwedge {\mathfrak g}\)
• On spectral triples in quantum gravity. II.
• Local and analytic cyclic homology
• A new spectral triple over a space of connections
• Index of a family of Dirac operators on loop space
• On the bundle of connections and the gauge orbit manifold in Yang-Mills theory
• On the Chern character of a theta-summable Fredholm module
• Generalized measures in gauge theory
• Functional integration on spaces of connections
• On the spectral characterization of manifolds
• On semi-classical states of quantum gravity and noncommutative geometry
• The local index formula in semifinite von Neumann algebras. I: Spectral flow
• Type II non-commutative geometry. I: Dixmier trace in von Neumann algebras
• Inverse Limits of Measure Spaces
• Holonomy loops, spectral triples and quantum gravity
• On spectral triples in quantum gravity: I
• Unbounded Fredholm Modules and Spectral Flow
• Quantum Gravity
• Lie theory and the Chern–Weil homomorphism
• Lie groups beyond an introduction

This page was built for publication: The JLO character for the noncommutative space of connections of Aastrup-Grimstrup-Nest