A computational approach of A ∞-(co)algebras

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 th...

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Bibliographic Details
Published in:International journal of computer mathematics 2010-03, Vol.87 (4), p.935-953
Main Author: Berciano-Alcaraz, Ainhoa
Format: Article
Language:English
Subjects:
55-04
Algebra
Algorithms
basic perturbation lemma
Computer programming
contraction
homological perturbation theory
Mathematical problems
software
symbolic computation
Topology
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Summary: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.
ISSN:0020-7160
1029-0265
DOI:10.1080/00207160802247612