On the Notion of Noncommutative Submanifold
Quantum Algebra
2020-06-11 v2
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 is a quotient algebra such that all derivations of can be lifted to . 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
Cite
@article{arxiv.1912.01225,
title = {On the Notion of Noncommutative Submanifold},
author = {Francesco D'Andrea},
journal= {arXiv preprint arXiv:1912.01225},
year = {2020}
}