Riemann surfaces and AF-algebras

Abstract

For a generic set in the Teichmueller space, we construct a covariant functor with the range in a category of the AF-algebras; the functor maps isomorphic Riemann surfaces to the stably isomorphic AF-algebras. As a special case, one gets a categorical correspondence between complex tori and the so-called Effros-Shen algebras.

to appear Annals of Functional Analysis. arXiv admin note: substantial text overlap with arXiv:math/0104077

References in corpus (3)

• Notes on A-infinity algebras, A-infinity categories and non-commutative geometry. I
• Classification of holomorphic vector bundles on noncommutative two-tori
• Quasicoherent sheaves on complex noncommutative two-tori

Cited by in corpus (1)

• On cluster C*-algebras