Slawomir Klimek, Matt McBride, Sumedha Rathnayake, Kaoru Sakai, Honglin Wang, “Derivations and Spectral Triples on Quantum Domains I: Quantum Disk”, SIGMA, 2017, Volume 13,075, 26 pp.

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SIGMA, 2017 Volume 13, 075, 26 pp. (Mi sigma1275)

This article is cited in 2 papers

Derivations and Spectral Triples on Quantum Domains I: Quantum Disk

Slawomir Klimek^a, Matt McBride^b, Sumedha Rathnayake^c, Kaoru Sakai^a, 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

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.

Keywords: invariant and covariant derivations; spectral triple; quantum disk.

MSC: 46L87; 46L89; 58B34; 58J42

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

Language: English

DOI: 10.3842/SIGMA.2017.075

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