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On the Notion of Noncommutative Submanifold
Symmetry, integrability and geometry: methods and applications, Tome 16 (2020) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {Francesco D'Andrea},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a49/}
}
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Francesco D'Andrea. On the Notion of Noncommutative Submanifold. Symmetry, integrability and geometry: methods and applications, Tome 16 (2020). http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a49/

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