Noncommutative elliptic theory. Examples

Abstract

We study differential operators, whose coefficients define noncommutative algebras. As algebra of coefficients, we consider crossed products, corresponding to action of a discrete group on a smooth manifold. We give index formulas for Euler, signature and Dirac operators twisted by projections over the crossed product. Index of Connes operators on the noncommutative torus is computed.

23 pages, 1 figure

References in corpus (4)

• Noncommutative Manifolds the Instanton Algebra and Isospectral Deformations
• Noncommutative finite-dimensional manifolds. I. Spherical manifolds and related examples
• Principal fibrations from noncommutative spheres
• Principal fibrations over noncommutative spheres

Cited by in corpus (3)

• Curved noncommutative torus and Gauss--Bonnet
• Analytic and algebraic indices of elliptic operators associated with discrete groups of quantized canonical transformations
• Elliptic theory for operators associated with diffeomorphisms of smooth manifolds