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arXiv · hep-th/9507148

Noncommutative Lattices and Their Continuum Limits

G. Bimonte·E. Ercolessi·G. Landi·F. Lizzi·G. Sparano·P. Teotonio-Sobrinho
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Abstract

We consider finite approximations of a topological space $M$ by noncommutative lattices of points. These lattices are structure spaces of noncommutative $C^*$-algebras which in turn approximate the algebra $\cc(M)$ of continuous functions on $M$. We show how to recover the space $M$ and the algebra $\cc(M)$ from a projective system of noncommutative lattices and an inductive system of noncommutative $C^*$-algebras, respectively.

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G. Bimonte, E. Ercolessi, G. Landi, F. Lizzi, G. Sparano, P. Teotonio-Sobrinho. 1995-09-28. Noncommutative Lattices and Their Continuum Limits. https://doi.org/10.1016/s0393-0440(95)00064-x

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