Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9495986 | Journal of Functional Analysis | 2005 | 31 Pages |
Abstract
We establish that, given a compact Abelian group G endowed with a continuous length function l and a sequence (Hn)nâN of closed subgroups of G converging to G for the Hausdorff distance induced by l, then C*G^,Ï is the quantum Gromov-Hausdorff limit of any sequence C*Hn^,ÏnnâN for the natural quantum metric structures and when the lifts of Ïn to G^ converge pointwise to Ï. This allows us in particular to approximate the quantum tori by finite-dimensional C*-algebras for the quantum Gromov-Hausdorff distance. Moreover, we also establish that if the length function l is allowed to vary, we can collapse quantum metric spaces to various quotient quantum metric spaces.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Frédéric Latrémolière,