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2009

Distances between matrix algebras that converge to coadjoint orbits

Rieffel, Marc A.

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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.

Distances between matrix algebras that converge to coadjoint orbits · Around

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David Kerr, Matricial quantum Gromov-Hausdorff distance , J. Funct. Anal. 205
2003
Earlier work this paper cites.
Marc A. Rieffel, Gromov-Hausdorff distance for quantum metric spaces , Mem. Amer. Math. Soc. 168
2004
Earlier work this paper cites.
by same author, Matrix algebras converge to the sphere for quantum Gromov-Hausdorff distance , Mem. Amer. Math. Soc. 168
2004
Earlier work this paper cites.

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Hanfeng Li, Order-unit quantum Gromov-Hausdorff distance , J. Funct. Anal. 231
2006
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Wei Wu, Quantized Gromov-Hausdorff distance , J. Funct. Anal. 238
2006
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by same author, C*-algebraic quantum Gromov-Hausdorff distance , arXiv:math.OA/0312003
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by same author, Vector bundles and Gromov-Hausdorff distance , J. K-Theory, to appear, arXiv:math.MG/0608266
Cited in the paper.
by same author, Leibniz seminorms for “Matrix algebras converge to the sphere” , arXiv:0707.3229
Original
Cited in the paper.

Then

David Kerr and Hanfeng Li, On Gromov-Hausdorff convergence for operator metric spaces , J. Operator Theory 62
2009
Closest in time.
by same author, Metric aspects of noncommutative homogeneous spaces , J. Funct. Anal. 257 (2009), no. 7, 2325–2350, arXiv:0810.4694
Original
2009
Closest in time.

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