Zilber, Boris Noncommutative Zariski geometries and their classical limit. (English) Zbl 1208.03042 Confluentes Math. 2, No. 2, 265-291 (2010). 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. Cited in 4 Documents MSC: 03C98 Applications of model theory 14A22 Noncommutative algebraic geometry 46L89 Other “noncommutative” mathematics based on \(C^*\)-algebra theory Keywords:nonclassical Zariski geometries; noncommutative \(C^*\)-algebras; natural limit construction; gauge field over two-dimensional Riemann surface PDFBibTeX XMLCite \textit{B. Zilber}, Confluentes Math. 2, No. 2, 265--291 (2010; Zbl 1208.03042) Full Text: DOI arXiv