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Item Derivations and Spectral Triples on Quantum Domains I: Quantum Disk(2017) Klimek, Slawomir; McBride, Matt; Rathnayake, Sumedha; Sakai, Kaoru; Wang, Honglin; Mathematical Sciences, School of ScienceWe 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.