๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Distances in finite spaces from noncommutative geometry

โœ Scribed by Bruno Iochum; Thomas Krajewski; Pierre Martinetti

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
190 KB
Volume
37
Category
Article
ISSN
0393-0440

No coin nor oath required. For personal study only.

โœฆ Synopsis

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 finite commutative cases corresponding to a metric on a finite set, and also compute explicitly some distances associated to commutative or noncommutative algebras.

๐Ÿ“œ SIMILAR VOLUMES

Distance geometry in quasihypermetric sp
Distance geometry in quasihypermetric spaces. II
โœ Peter Nickolas; Reinhard Wolf ๐Ÿ“‚ Article ๐Ÿ“… 2010 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 135 KB

## Abstract Let (__X__, __d__) be a compact metric space and let ${\cal M}(X)$ denote the space of all finite signed Borel measures on __X__. Define \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$I :{\cal M}(X)\rightarrow {\mathbb R}$\end{document} by __I__(ฮผ) = โˆซ~__X_

Distance geometry in quasihypermetric sp
Distance geometry in quasihypermetric spaces. III
โœ Peter Nickolas; Reinhard Wolf ๐Ÿ“‚ Article ๐Ÿ“… 2011 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 157 KB

## Abstract Let (__X__, __d__) be a compact metric space and let \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$\mathcal {M}(X)$\end{document} denote the space of all finite signed Borel measures on __X__. Define \documentclass{article}\usepackage{amssymb}\pagestyle{em

Classification of Embeddings of the Flag
Classification of Embeddings of the Flag Geometries of Projective Planes in Finite Projective Spaces, Part 1
โœ Joseph A. Thas; Hendrik Van Maldeghem ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 156 KB

The flag geometry 1=(P, L, I) of a finite projective plane 6 of order s is the generalized hexagon of order (s, 1) obtained from 6 by putting P equal to the set of all flags of 6, by putting L equal to the set of all points and lines of 6, and where I is the natural incidence relation (inverse conta