Abstract
We study property T for an action α of a discrete group Γ on a unital C*-algebra \(\mathscr{A}\). Our main results improve some well-known results about property T for groups. Moreover, we introduce Hilbert \(\mathscr{A}\)-module property T and show that the action α has property T if and only if the reduced crossed product \(\mathscr{A}\;{\rtimes_{\alpha, r}}\) Γ has Hilbert \(\mathscr{A}\)-module property T.
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Supported by the National Natural Science Foundation of China (Grant Nos. 11871303, 11671133 and 11701327), Natural Science Foundation of Shandong Province (Grant No. ZR2019MA039), the China Postdoctoral Science Foundation (Grant No. 2018M642633) and a Project of Shandong Province Higher Educational Science and Technology Program (Grant No. J18KA238)
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Meng, Q., Wang, L.G. Property T for Actions. Acta. Math. Sin.-English Ser. 35, 1807–1816 (2019). https://doi.org/10.1007/s10114-019-9024-y
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DOI: https://doi.org/10.1007/s10114-019-9024-y