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 is a quotient algebra such that all derivations of can be lifted to . We will argue that in the case of smooth functions on manifolds,...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2020 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2020
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210700 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On the Notion of Noncommutative Submanifold. Francesco D'Andrea. SIGMA 16 (2020), 050, 21 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862590982020661248 |
|---|---|
| author | D'Andrea, Francesco |
| author_facet | D'Andrea, Francesco |
| citation_txt | On the Notion of Noncommutative Submanifold. Francesco D'Andrea. SIGMA 16 (2020), 050, 21 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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 is a quotient algebra such that all derivations of can be lifted to . 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.
|
| first_indexed | 2025-12-17T12:03:41Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210700 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-17T12:03:41Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | 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 is a quotient algebra such that all derivations of can be lifted to . 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 |
| spellingShingle | On the Notion of Noncommutative Submanifold D'Andrea, Francesco |
| title | 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_short | On the Notion of Noncommutative Submanifold |
| title_sort | on the notion of noncommutative submanifold |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210700 |
| work_keys_str_mv | AT dandreafrancesco onthenotionofnoncommutativesubmanifold |