On the Notion of Noncommutative Submanifold
We review the notion of submanifold algebra, as introduced by T. Masson, and discuss some properties and examples. A submanifold algebra of an associative algebra 𝘈 is a quotient algebra 𝘉 such that all derivations of 𝘉 can be lifted to 𝘈. We will argue that in the case of smooth functions on manifo...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2020 |
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| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210700 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On the Notion of Noncommutative Submanifold. Francesco D'Andrea. SIGMA 16 (2020), 050, 21 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-210700 |
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D'Andrea, Francesco 2025-12-15T15:24:18Z 2020 On the Notion of Noncommutative Submanifold. Francesco D'Andrea. SIGMA 16 (2020), 050, 21 pages 1815-0659 2020 Mathematics Subject Classification: 46L87; 53C99; 53D55; 13N15 arXiv:1912.01225 https://nasplib.isofts.kiev.ua/handle/123456789/210700 https://doi.org/10.3842/SIGMA.2020.050 We review the notion of submanifold algebra, as introduced by T. Masson, and discuss some properties and examples. A submanifold algebra of an associative algebra 𝘈 is a quotient algebra 𝘉 such that all derivations of 𝘉 can be lifted to 𝘈. We will argue that in the case of smooth functions on manifolds, every quotient algebra is a submanifold algebra, derive a topological obstruction when the algebras are deformation quantizations of symplectic manifolds, present some (commutative and noncommutative) examples and counterexamples. I would like to thank Alessandro De Paris for suggesting Example 17 and Chiara Esposito for her comments on a preliminary version of the paper. A special thanks goes to the anonymous referees for carefully reading the paper and suggesting some interesting future research lines. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On the Notion of Noncommutative Submanifold Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On the Notion of Noncommutative Submanifold |
| spellingShingle |
On the Notion of Noncommutative Submanifold D'Andrea, Francesco |
| title_short |
On the Notion of Noncommutative Submanifold |
| title_full |
On the Notion of Noncommutative Submanifold |
| title_fullStr |
On the Notion of Noncommutative Submanifold |
| title_full_unstemmed |
On the Notion of Noncommutative Submanifold |
| title_sort |
on the notion of noncommutative submanifold |
| author |
D'Andrea, Francesco |
| author_facet |
D'Andrea, Francesco |
| publishDate |
2020 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We review the notion of submanifold algebra, as introduced by T. Masson, and discuss some properties and examples. A submanifold algebra of an associative algebra 𝘈 is a quotient algebra 𝘉 such that all derivations of 𝘉 can be lifted to 𝘈. We will argue that in the case of smooth functions on manifolds, every quotient algebra is a submanifold algebra, derive a topological obstruction when the algebras are deformation quantizations of symplectic manifolds, present some (commutative and noncommutative) examples and counterexamples.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210700 |
| citation_txt |
On the Notion of Noncommutative Submanifold. Francesco D'Andrea. SIGMA 16 (2020), 050, 21 pages |
| work_keys_str_mv |
AT dandreafrancesco onthenotionofnoncommutativesubmanifold |
| first_indexed |
2025-12-17T12:03:41Z |
| last_indexed |
2025-12-17T12:03:41Z |
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1851756926634819584 |