English

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 AA is a quotient algebra BB such that all derivations of BB can be lifted to AA. 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}
}