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On the Smoothness of the Noncommutative Pillow and Quantum Teardrops
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- Symmetry, Integrability and Geometry: Methods and Applications, 2014, том 10
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On the Smoothness of the Noncommutative Pillow and Quantum Teardrops
Інший ID:
2010 Mathematics Subject Classification: 58B32; 58B34
DOI:10.3842/SIGMA.2014.015
DOI:10.3842/SIGMA.2014.015
Посилання:
On the Smoothness of the Noncommutative Pillow and Quantum Teardrops / T. Brzeziński // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 21 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Noncommutative Geometry and Quantum Groups in
honor of Marc A. Rief fel. The full collection is available at http://www.emis.de/journals/SIGMA/Rieffel.html.
I would like to thank Ulrich Kr¨ahmer for discussions, Li-Yu Liu for bringing reference [14] to
my attention, and Piotr M. Hajac and the referees for helpful comments. I am grateful to
Fields Institute for Research in Mathematical Sciences in Toronto, where these results were first
presented, for creating excellent research environment and for support.
Дата:
2014
Переглядів:
473
Завантажень:
225
Анотація:
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(Σ³q) [J. Geom. Phys. 62 (2012), 1097-1107], quantum real weighted projective planes O(RP²q(l;±)) [PoS Proc. Sci. (2012), PoS(CORFU2011), 055, 10 pages] and quantum Seifert lens spaces O(Σ³q(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.
