The Haagerup property for twisted groupoid dynamical systems

Kwasniewski BK, Li K, Skalski A (2022)

Publication Type: Journal article

Publication year: 2022


Book Volume: 283

Journal Issue: 1

DOI: 10.1016/j.jfa.2022.109484


We introduce the Haagerup property for twisted groupoid C*-dynamical systems in terms of naturally defined positive definite operator-valued multipliers. By developing a version of 'the Haagerup trick' we prove that this property is equivalent to the Haagerup property of the reduced crossed product C*-algebra with respect to the canonical conditional expectation E. This extends a theorem of Dong and Ruan for discrete group actions, and implies that a given Cartan inclusion of separable C*-algebras has the Haagerup property if and only if the associated Weyl groupoid has the Haagerup property in the sense of Tu. We use the latter statement to prove that every separable C*-algebra which has the Haagerup property with respect to some Cartan subalgebra satisfies the Universal Coefficient Theorem. This generalises a recent result of Barlak and Li on the UCT for nuclear Cartan pairs. (C) 2022 Elsevier Inc. All rights reserved.

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Kwasniewski, B.K., Li, K., & Skalski, A. (2022). The Haagerup property for twisted groupoid dynamical systems. Journal of Functional Analysis, 283(1).


Kwasniewski, Bartosz K., Kang Li, and Adam Skalski. "The Haagerup property for twisted groupoid dynamical systems." Journal of Functional Analysis 283.1 (2022).

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