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This article is cited in 4 scientific papers (total in 4 papers)
On the Notion of Noncommutative Submanifold
Francesco D'Andreaab a I.N.F.N. Sezione di Napoli, Complesso MSA, Via Cintia, 80126 Napoli, Italy
b Università di Napoli ''Federico II'', Napoli, Italy
Abstract:
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.
Keywords:
submanifold algebras, tangential star products, coisotropic reduction.
Received: January 11, 2020; in final form May 30, 2020; Published online June 9, 2020
Citation:
Francesco D'Andrea, “On the Notion of Noncommutative Submanifold”, SIGMA, 16 (2020), 050, 21 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1587 https://www.mathnet.ru/eng/sigma/v16/p50
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Abstract page: | 56 | Full-text PDF : | 37 | References: | 10 |
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