On the Notion of Noncommutative Submanifold

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dc.contributor.authorD'Andrea, Francesco
dc.date.accessioned2025-12-15T15:24:18Z
dc.date.issued2020
dc.description.abstractWe 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.
dc.description.sponsorshipI 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.
dc.identifier.citationOn the Notion of Noncommutative Submanifold. Francesco D'Andrea. SIGMA 16 (2020), 050, 21 pages
dc.identifier.doihttps://doi.org/10.3842/SIGMA.2020.050
dc.identifier.issn1815-0659
dc.identifier.other2020 Mathematics Subject Classification: 46L87; 53C99; 53D55; 13N15
dc.identifier.otherarXiv:1912.01225
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/210700
dc.language.isoen
dc.publisherІнститут математики НАН України
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlier
dc.titleOn the Notion of Noncommutative Submanifold
dc.typeArticle

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Symmetry, Integrability and Geometry: Methods and Applications, 2020, том 16, випуск за цей рік