KU-SDU operator algebra seminar (online)
The study of metrics on state spaces arising from semi-norms dates back to Connes and was formalised as the notion of a compact quantum metric space by Rieffel, whose notion of quantum Gromov-Hausdorff distance on the class of compact quantum metric spaces, has established a new famework for the study of approximations of C*-algebras.
In a recent paper, Aguilar and Kaad have shown that the standard Podleś sphere, originally introduced as the homogeneous space for Woronowicz' quantum SU(2), is in fact a compact quantum metric space, and they posed the rather natural question, whether the standard Podleś sphere converges to the standard 2-sphere in the quantum analogues of the Gromov-Hausdorff distance as the deformation parameter tends to 1.
In my talk I will give a short introduction to the theory of compact quantum metric spaces, and present some new developments to the above question based on joint work with Jens Kaad and David Kyed, In particular we have shown that the commutative C*-subalgebras generated by the self-adjoint generator of the standard Podleś sphere, converge to the interval of length \pi, paving the way for a solution to the more general question which was proven very recently by Aguilar, Kaad and Kyed.
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