Journal of Operator Theory

Volume 95, Issue 2, Spring 2026 pp. 505-518.

Equivariant $\mathcal{D}$-stability for actions of tensor categories

Authors: Samuel Evington (1), Sergio Giron Pacheco (2), Corey Jones (3)
Author institution: (1) Mathematical Institute, University of Muenster, Einsteinstrasse 62, 48149 Muenster, Germany
(2) Department of mathematics, KU Leuven, Celestijnenlaan 200B, 3001, Leuven, Belgium
(3) Department of Mathematics, North Carolina State University, North Carolina, U.S.A.

Summary: We introduce a notion of equivariant $\mathcal{D}$-stability for actions of unitary tensor categories on $C^*$-algebras. We show that, when $\mathcal{D}$ is strongly self-absorbing, equivariant $\mathcal{D}$-stability of an action is equivalent to a unital embedding of $\mathcal{D}$ into a certain subalgebra of Kirchberg's central sequence algebra. We use this to show $\mathcal{Z}$-stability for a large class of AF-actions.

DOI: http://dx.doi.org/10.7900/jot.2024jul12.2480
Keywords: unitary tensor category, $\mathcal{Z}$-stability, classification

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