On the Smoothness of the Noncommutative Pillow and Quantum Teardrops
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],...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2014 |
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Інститут математики НАН України
2014
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| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862672162352005120 |
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| author | Brzeziński, T. |
| author_facet | Brzeziński, T. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-07T15:35:02Z |
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| id | nasplib_isofts_kiev_ua-123456789-146840 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
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| publishDate | 2014 |
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| spelling | Brzeziński, T. 2019-02-11T17:04:23Z 2019-02-11T17:04:23Z 2014 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. 1815-0659 2010 Mathematics Subject Classification: 58B32; 58B34 DOI:10.3842/SIGMA.2014.015 https://nasplib.isofts.kiev.ua/handle/123456789/146840 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On the Smoothness of the Noncommutative Pillow and Quantum Teardrops Article published earlier |
| spellingShingle | On the Smoothness of the Noncommutative Pillow and Quantum Teardrops Brzeziński, T. |
| title | On the Smoothness of the Noncommutative Pillow and Quantum Teardrops |
| title_full | On the Smoothness of the Noncommutative Pillow and Quantum Teardrops |
| title_fullStr | On the Smoothness of the Noncommutative Pillow and Quantum Teardrops |
| title_full_unstemmed | On the Smoothness of the Noncommutative Pillow and Quantum Teardrops |
| title_short | On the Smoothness of the Noncommutative Pillow and Quantum Teardrops |
| title_sort | on the smoothness of the noncommutative pillow and quantum teardrops |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146840 |
| work_keys_str_mv | AT brzezinskit onthesmoothnessofthenoncommutativepillowandquantumteardrops |