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],...

Повний опис

Збережено в:
Бібліографічні деталі
Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2014
Автор: Brzeziński, T.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2014
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/146840
Теги: Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати: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.

Репозитарії

Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-146840
record_format dspace
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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title On the Smoothness of the Noncommutative Pillow and Quantum Teardrops
spellingShingle On the Smoothness of the Noncommutative Pillow and Quantum Teardrops
Brzeziński, T.
title_short 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_sort on the smoothness of the noncommutative pillow and quantum teardrops
author Brzeziński, T.
author_facet Brzeziński, T.
publishDate 2014
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/146840
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.
work_keys_str_mv AT brzezinskit onthesmoothnessofthenoncommutativepillowandquantumteardrops
first_indexed 2025-12-07T15:35:02Z
last_indexed 2025-12-07T15:35:02Z
_version_ 1850864254087856128