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Theoretical analysis demonstrates fixed-point algebra equivalence to Cartan subalgebras in localized Bost-Connes systems, indicating dynamical isomorphisms reduce to underlying groupoid data.
For localized Bost-Connes C*-dynamical systems the fixed-point algebra of the gauge action is identified with the canonical Cartan subalgebra, and equivariant isomorphisms of the systems are shown to be governed by this identification: an equivariant rigidity theorem reducing dynamical isomorphism to the underlying groupoid data.
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Ruqing Chen (2026) studied this question.
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