Dirac operator on a noncommutative Toeplitz torus

TL;DR

This paper constructs a spectral triple for a noncommutative torus within the Toeplitz algebra framework, advancing the understanding of noncommutative geometric structures.

Contribution

It introduces a 1+ summable regular even spectral triple for a noncommutative torus derived from a Toeplitz algebra subalgebra, a novel approach in noncommutative geometry.

Findings

Spectral triple constructed for noncommutative torus

Demonstrates 1+ summability and regularity

Provides new insights into Toeplitz algebra-based noncommutative spaces

Abstract

We construct a 1+ summable regular even spectral triple for a noncommutative torus defined by a C*-subalgebra of the Toeplitz algebra.