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Preprint Number 850

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850. Masanori Itai and Boris Zilber
Notes on a model theory of quantum 2-torus for generic q

Submission date: 20 March 2015.


We describe a structure over the complex numbers associated with the non-commutative algebra Aq called quantum 2-tori. These turn out to have uncountably categorical L_omega1,omega-theory, and are similar to other pseudo-analytic structures considered by the second author. The first-order theory of a quantum torus for generic q interprets arithmetic and so is unstable and undecidable. But certain interesting reduct of the structure, a quantum line bundle, is superstable.

Mathematics Subject Classification: 03C30 (Primary), 03C45, 03C50 (Secondary)

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Full text arXiv 1503.06045: pdf, ps.

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