TY  - JOUR
AU  - Qiang, Xiangqi
PY  - 2026
TI  - Continuous orbit equivalence of groupoid actions
JO  - AIMS Mathematics
SP  - 13287
EP  - 13303
VL  - 11
IS  - 5
AB  - In this paper, I studied continuous actions of étale groupoids on compact Hausdorff spaces and the associated operator algebras. I introduced notions of conjugacy and continuous orbit equivalence for such groupoid actions and characterized them in terms of the corresponding transformation groupoids and their reduced        C    ∗  -algebras. In particular, I proved that two topologically free actions are continuously orbit equivalent if and only if their associated transformation groupoid        C    ∗  -algebras are isomorphic, and if and only if there exists a        C    ∗  -algebra isomorphism preserving the canonical Cartan subalgebras between the corresponding reduced        C    ∗  -algebras of these transformation groupoids.
UR  - https://doi.org/10.3934/math.2026548
DO  - 10.3934/math.2026548