1999/12/22 by Bruno Iochum, B. Iochum, Thomas Krajewski +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Commutative property #Holomorphic and Operator Theory #Metric (unit) #Noncommutative algebraic geometry #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Quantum differential calculus #Spectral triple #gr-qc #hep-th #math-ph #math.MP #math.OA
paper · pdf · doi:10.1016/s0393-0440(00)00044-9
published as J.Geom.Phys. 37 (2001) 100-125 · 27 pages, 2 figures
arxiv created 1999/12/22 · openalex publication_date 2001/01/01 · arxiv updated 2015/06/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Following the general principles of noncommutative geometry, it is possible to define a metric on the space of pure states of the noncommutative algebra generated by the coordinates. This metric generalizes the usual Riemannian one. We investigate some general properties of this metric in the finite commutative case which corresponds to a metric on a finite set, and also give some examples of computations in both commutative and noncommutative cases.