Distances between matrix algebras that converge to coadjoint orbits

TL;DR

This paper provides explicit formulas for the convergence of distances between matrix algebras and coadjoint orbits, viewed as quantum metric spaces, and introduces a general approach applicable to similar contexts.

Contribution

It introduces explicit formulas for distances between matrix algebras converging to coadjoint orbits and develops a general framework for analyzing such quantum metric space convergence.

Findings

Distances between matrix algebras and coadjoint orbits converge to zero.

Explicit formulas for these distances are provided.

A general approach for similar convergence problems is developed.

Abstract

For any sequence of matrix algebras that converge to a coadjoint orbit we give explicit formulas that show that the distances between the matrix algebras (viewed as quantum metric spaces) converges to 0. In the process we develop a general point of view that is likely to be useful in other related settings.