$C^*$-diagonal of inductive limit of $1$-dimensional NCCW complexes

Dolapo Oyetunbi

$C^*$-diagonal of inductive limit of $1$-dimensional NCCW complexes

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arxiv 2505.04011 v1 pith:WLIYFHY6 submitted 2025-05-06 math.OA

Dolapo Oyetunbi This is my paper · ORCID

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keywords complexesdiagonaldimensionalinductivelimitnccwapproximatingestablishes

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abstract

This paper establishes the existence of a $C^*$-diagonal in the inductive limit of 1-dimensional NCCW complexes with trivial $K_1$-groups. It also examines some limitations and implications of approximating $^*$-homomorphisms between two such complexes.

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A C*-diagonal in the Jiang-Su algebra via entangled matrix cones
math.OA 2026-07 accept novelty 7.0 of 10

An explicit inductive system of entangled dimension-drop algebras realises Z and yields a C*-diagonal with one-dimensional non-locally-connected spectrum, via a new normaliser characterisation by state excision.

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