Blackbox computation of $A_\infty$-algebras

TL;DR

This paper proves that for a certain class of dg-algebras, an algorithm based on Kadeishvili's proof can finitely compute a complete $A_ abla$-algebra structure on their homology, advancing computational methods in algebra.

Contribution

It demonstrates that the inductive algorithm for $A_ abla$-algebra structures terminates finitely for a specific class of dg-algebras, providing a practical computational approach.

Findings

Finite termination of the algorithm for the class of dg-algebras considered

Complete $A_ abla$-algebra structures can be generated after finite steps

Advancement in computational algebra for $A_ abla$-structures

Abstract

Kadeishvili's proof of the minimality theorem induces an algorithm for the inductive computation of an $A_\infty$-algebra structure on the homology of a dg-algebra. In this paper, we prove that for one class of dg-algebras, the resulting computation will generate a complete $A_\infty$-algebra structure after a finite amount of computational work.