L₂-cohomology, derivations and quantum Markov semi-groups on q-Gaussian algebras

2019/05/28 by Caspers, Martijn, Isono, Yusuke, Wasilewski, Mateusz · 1 citation
#FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1905.11619

Abstract

We study (quasi-)cohomological properties through an analysis of quantum Markov semi-groups. We construct higher order Hochschild cocycles using gradient forms associated with a quantum Markov semi-group. By using Schatten-S_p estimates we analyze when these cocycles take values in the coarse bimodule. For the 1-cocycles (the derivations) we show that under natural conditions they imply the Akemann-Ostrand property (using the Riesz transform). We apply this to q-Gaussian algebras Γ_q(H). As a result q-Gaussians satisfy AO⁺ for | q | \leqslant dim(H)^-1/2. This includes a new range of q in low dimensions compared to Shlyakhtenko.

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• W*-correlations of II₁ factors and rigidity of tensor products and graph products

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