On the Smoothness of the Noncommutative Pillow and Quantum Teardrops
نویسندگان
چکیده
Recent results by Krähmer [Israel J. Math. 189 (2012), 237–266] on smoothness of Hopf–Galois extensions and by Liu [arXiv:1304.7117] on smoothness of generalized Weyl algebras are used to prove that the coordinate algebras of the noncommutative pillow orbifold [Internat. J. Math. 2 (1991), 139–166], quantum teardrops O(WPq(1, l)) [Comm. Math. Phys. 316 (2012), 151–170], quantum lens spaces O(Lq(l; 1, l)) [Pacific J. Math. 211 (2003), 249–263], the quantum Seifert manifold O(Σq) [J. Geom. Phys. 62 (2012), 1097–1107], quantum real weighted projective planes O(RPq(l;±)) [PoS Proc. Sci. (2012), PoS(CORFU2011), 055, 10 pages] and quantum Seifert lens spaces O(Σq(l;−)) [Axioms 1 (2012), 201–225] are homologically smooth in the sense that as their own bimodules they admit finitely generated projective resolutions of finite length.
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