Deformation Quantization of A-infinity Equivalences

TL;DR

This paper demonstrates that deformation quantization preserves $A_ $-Morita equivalences between Koszul dual $A_ $-algebras, highlighting stability of algebraic structures under quantization.

Contribution

It establishes that quadratic Poisson structures' deformation quantization maintains $A_ $-Morita equivalences, a novel result in the context of $A_ $-algebra theory.

Findings

Deformation quantization preserves $A_ $-Morita equivalence.

Quadratic Poisson structures are compatible with $A_ $-algebra equivalences.

The result applies to Koszul dual $A_ $-algebras.

Abstract

We show that Deformation Quantization of quadratic Poisson structures preserves the $A_\infty$-Morita equivalence of a given pair of Koszul dual $A_\infty$-algebras.