Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 10 (2014), 036, 15 pages      arXiv:1309.7096      https://doi.org/10.3842/SIGMA.2014.036

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

Slawomir Klimek a and 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

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

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.

Key words: Dirac type operator; quantum space, C*-algebra.

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