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

SIGMA 13 (2017), 075, 26 pages      arXiv:1705.04005      https://doi.org/10.3842/SIGMA.2017.075

Derivations and Spectral Triples on Quantum Domains I: Quantum Disk

Slawomir Klimek ^a, Matt McBride ^b, Sumedha Rathnayake ^c, Kaoru Sakai ^a and Honglin Wang ^a
a) Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, 402 N. Blackford St., Indianapolis, IN 46202, USA
^b) Department of Mathematics and Statistics, Mississippi State University, 175 President's Cir., Mississippi State, MS 39762, USA
^c) Department of Mathematics, University of Michigan, 530 Church St., Ann Arbor, MI 48109, USA

Received May 12, 2017, in final form September 21, 2017; Published online September 24, 2017

Abstract
We study unbounded invariant and covariant derivations on the quantum disk. In particular we answer the question whether such derivations come from operators with compact parametrices and thus can be used to define spectral triples.

Key words: invariant and covariant derivations; spectral triple; quantum disk.

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