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arXiv · 2510.18021

Compactification of quasi-local algebras on the lattice

Jun Ikeda
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Abstract

We introduce a compactification construction for abstract quasi-local C*-algebras over countable metric spaces equipped with an isometric group action which is functorial with respect to bounded spread isomorphisms. In $1$D, the construction recovers Ocneanu's Tube algebra for fusion spin chains, and provides a canonical bridge between infinite-volume observables and observables with periodic boundary conditions. We exploit this connection to derive an obstruction for the implementability of such topological symmetries as Kramers-Wannier type dualities on symmetric subalgebras.

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Jun Ikeda. 2025-10-20. Compactification of quasi-local algebras on the lattice. https://arxiv.org/abs/2510.18021

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