Topology Change and Vector Modules on Noncommutative Surfaces of Rotation

“Wick Rotations”: The Noncommutative Hyperboloids and Other Surfaces of Rotations

A “Wick rotation” is applied to the noncommutative sphere to produce a noncommutative version of the hyperboloids. A harmonic basis of the associated algebra is given. It is noted that, for the one sheeted hyperboloid, the vector space for the noncommutative algebra can be completed to a Hilbert space, where multiplication is not continuous. A method of constructing noncommutative analogues of ...

Zariski-Like Topology on the Classical Prime Spectrum of a Modules

On two problems concerning the Zariski topology of modules

Let $R$ be an associative ring and let $M$ be a left $R$-module.Let $Spec_{R}(M)$ be the collection of all prime submodules of $M$ (equipped with classical Zariski topology). There is a conjecture which says that every irreducible closed subset of $Spec_{R}(M)$ has a generic point. In this article we give an affirmative answer to this conjecture and show that if $M$ has a Noetherian spectrum, t...

ar X iv : h ep - t h / 01 01 09 3 v 1 1 5 Ja n 20 01 C ∗ algebras and Differential Geometry ∗

This is the translation to appear in the ”SUPERSYMMETRY 2000 Encyclopaedic Dictionary” of the original Comptes Rendus Note, published in March 1980, in which basic notions of noncommutative geometry were introduced and applied to noncommutative tori. These include connections on finite projective modules, their curvature, and the Chern character. Finite projective modules on the noncommutative ...

Poincaré Duality and Spinc Structures for Complete Noncommutative Manifolds

We prove a noncompact Serre-Swan theorem characterising modules which are sections of vector bundles not necessarily trivial at infinity. We then identify the endomorphism algebras of the resulting modules. The endomorphism results continue to hold for the generalisation of these modules to noncommutative, nonunital algebras. Finally, we apply these results to not necessarily compact noncommuta...