Abstract
We construct a class of C*-metric algebras. We prove that for a discrete group Γ with a 2-cocycle σ, the closure of the seminorm ∥[Mℓ, ·]∥ on Cc(Γ, σ) is a Leibniz Lip-norm on the twisted reduced group C*-algebra Cr*(Γ, σ) for the pointwise multiplication operator Mℓ on ℓ2(Γ), induced by a proper length function ℓ on Γ with the property of bounded θ-dilation. Moreover, the compact quantum metric space structures depend only on the cohomology class of 2-cocycles in the Lipschitz isometric sense.
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Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant Nos. 11171109 and 11801177) and the Science and Technology Commission of Shanghai Municipality (Grant No. 18dz2271000).
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Long, B., Wu, W. Twisted bounded-dilation group C*-algebras as C*-metric algebras. Sci. China Math. 64, 547–572 (2021). https://doi.org/10.1007/s11425-017-9418-x
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DOI: https://doi.org/10.1007/s11425-017-9418-x
Keywords
- discrete group
- bounded θ-dilation
- twisted reduced group C*-algebra
- C*-metric algebra
- Leibniz Lip-norm
- compact quantum metric space