A computational approach of A_∞-(co)algebras

Abstract

We present a computer program to compute the explicit structural components of an A _∞-(co)algebra deduced from a contraction, which is a special type of homotopy equivalence. The input is a contraction from a dg-(co)algebra to a simple dg-module and the output is a functional object that defines the operations {μ _i } _i≥1 (resp. {Δ _i } _i≥1) in the deduced A _∞-structure on the simple dg-module. We conclude with some concrete applications.

Keywords:

• homological perturbation theory
• contraction
• basic perturbation lemma
• symbolic computation
• software

2000 AMS Subject Classification :

• 55P43
• 68W30
• 55-04
• 55U05

Acknowledgements

This work was partially supported by a project of University of the Basque Country ‘EHU06/05’ and by PAICYT research project FQM-296.