PreprintCC BY 4.0arXiv
Morphisms of A∞-algebras and modules
Abstract
A∞-algebra is a chain complex equipped with a coherent multiplicative structure, i.e. a multiplication which is commutative up to (higher) chain homotopy. Similarly A∞-module over such algebra is equipped with its coherent action. These notions are used to represent cohomological information contained in topological multiplicative structures. One of the key tools of the theory are minimal models, which are useful in cohomological computations. In this thesis author presents certain sufficient conditions for a morphism of A∞-modules to induce a morphism of their minimal models.
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BibTeX
@misc{malashchuk2026morphisms,
title = {{Morphisms of $A_\infty$-algebras and modules}},
author = {Mikhail Malashchuk},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06851},
eprint = {2611.06851},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06851},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Morphisms of A_∞-algebras and modules
AU - Mikhail Malashchuk
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06851
UR - https://arxiv.org/abs/2611.06851
AB - A_∞-algebra is a chain complex equipped with a coherent multiplicative structure, i.e. a multiplication which is commutative up to (higher) chain homotopy. Similarly A_∞-module over such algebra is equipped with its coherent action. These notions are used to represent cohomological information contained in topological multiplicative structures. One of the key tools of the theory are minimal models, which are useful in cohomological computations. In this thesis author presents certain sufficient conditions for a morphism of A_∞-modules to induce a morphism of their minimal models.
ER -