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Noncommutative Zariski geometries and their classical limit. (English) Zbl 1208.03042

Summary: We undertake a case study of two series of nonclassical Zariski geometries and show that these geometries can be realised as representations of certain noncommutative \(C^*\)-algebras. We introduce a natural limit construction which for each of the two series produces a classical \(U(1)\)-gauge field over a two-dimensional Riemann surface.

MSC:

03C98 Applications of model theory
14A22 Noncommutative algebraic geometry
46L89 Other “noncommutative” mathematics based on \(C^*\)-algebra theory
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