Slawomir Klimek, Matt McBride, “A Note on Gluing Dirac Type Operators on a Mirror Quantum Two-Sphere”, SIGMA, 2014, Volume 10,036, 15 pp.

This article is cited in 3 papers

A Note on Gluing Dirac Type Operators on a Mirror Quantum Two-Sphere

Slawomir Klimek^a, Matt McBride^b

^a Department of Mathematical Sciences, Indiana University–Purdue University Indianapolis, 402 N. Blackford St., Indianapolis, IN 46202, USA
^b Department of Mathematics, University of Oklahoma, 601 Elm St., Norman, OK 73019, USA

Abstract: The goal of this paper is to introduce a class of operators, which we call quantum Dirac type operators on a noncommutative sphere, by a gluing construction from copies of noncommutative disks, subject to an appropriate local boundary condition. We show that the resulting operators have compact resolvents, and so they are elliptic operators.

Keywords: Dirac type operator; quantum space, $C^*$-algebra.

MSC: 46L99; 47B99; 81R60

Received: September 30, 2013; in final form March 25, 2014; Published online March 29, 2014

Language: English

DOI: 10.3842/SIGMA.2014.036