On the Notion of Noncommutative Submanifold

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2020
• Main Author: D'Andrea, Francesco
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2020
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/210700
• 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

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...