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Metric aspects of noncommutative homogeneous spaces

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 نشر من قبل Hanfeng Li
 تاريخ النشر 2009
  مجال البحث
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 تأليف Hanfeng Li




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For a closed cocompact subgroup $Gamma$ of a locally compact group $G$, given a compact abelian subgroup $K$ of $G$ and a homomorphism $rho:hat{K}to G$ satisfying certain conditions, Landstad and Raeburn constructed equivariant noncommutative deformations $C^*(hat{G}/Gamma, rho)$ of the homogeneous space $G/Gamma$, generalizing Rieffels construction of quantum Heisenberg manifolds. We show that when $G$ is a Lie group and $G/Gamma$ is connected, given any norm on the Lie algebra of $G$, the seminorm on $C^*(hat{G}/Gamma, rho)$ induced by the derivation map of the canonical $G$-action defines a compact quantum metric. Furthermore, it is shown that this compact quantum metric space depends on $rho$ continuously, with respect to quantum Gromov-Hausdorff distances.



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