Dirac operators on noncommutative hypersurfaces

Abstract

This paper studies geometric structures on noncommutative hypersurfaces within a module-theoretic approach to noncommutative Riemannian (spin) geometry. A construction to induce differential, Riemannian and spinorial structures from a noncommutative embedding space to a noncommutative hypersurface is developed and applied to obtain noncommutative hypersurface Dirac operators. The general construction is illustrated by studying the sequence ${\mathbb{T}}_{\theta }^2\hookrightarrow {\mathbb{S}}_{\theta }^3\hookrightarrow {\mathbb{R}}_{\theta }^4$ of noncommutative hypersurface embeddings.

arXiv commentv2: 25 pages. Final version to appear in Journal of Geometry and Physics

References in corpus (6)

• Noncommutative Manifolds the Instanton Algebra and Isospectral Deformations
• An Introduction to Noncommutative Spaces and their Geometry
• Noncommutative finite-dimensional manifolds. I. Spherical manifolds and related examples
• Nonassociative geometry in quasi-Hopf representation categories I: Bimodules and their internal homomorphisms
• Finite spectral triples for the fuzzy torus
• Mapping spaces and automorphism groups of toric noncommutative spaces

Cited by in corpus (1)

• Twisted Quadrics and Algebraic Submanifolds in ${\mathbb{R}}^n$