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arXiv · 1912.01225

On the Notion of Noncommutative Submanifold

Francesco D'Andrea
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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.

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BibTeXRIS

Francesco D'Andrea. 2019-12-03. On the Notion of Noncommutative Submanifold. https://doi.org/10.3842/sigma.2020.050

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