Order-unit quantum Gromov-Hausdorff distance

Details Order-unit quantum Gromov-Hausdorff distance Order-unit quantum Gromov-Hausdorff distance

2003-11-28

arxiv.org/abs/math/0312001v3

J. Funct. Anal. 231 (2006), no. 2, 312--360.

Mathematics

Operator Algebras

42 pages. Proposition 4.7 is added. To apear in J. Funct. Anal

Scientific paper

We introduce a new distance dist_oq between compact quantum metric spaces. We show that dist_oq is Lipschitz equivalent to Rieffel's distance dist_q, and give criteria for when a parameterized family of compact quantum metric spaces is continuous with respect to dist_oq. As applications, we show that the continuity of a parameterized family of quantum metric spaces induced by ergodic actions of a fixed compact group is determined by the multiplicities of the actions, generalizing Rieffel's work on noncommutative tori and integral coadjoint orbits of semisimple compact connected Lie groups; we also show that the theta-deformations of Connes and Landi are continuous in the parameter theta.

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