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Derived homotopy algebras

Part of: Applied homological algebra and category theory

Published online by Cambridge University Press:  25 July 2022

Jeroen Maes  and
Fernando Muro Open the ORCID record for Fernando Muro [Opens in a new window]
Jeroen Maes
Affiliation:
Facultad de Matemáticas, Departamento de Álgebra, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012 Sevilla, Spain (fmuro@us.es), http://personal.us.es/fmuro
Fernando Muro
Affiliation:
Facultad de Matemáticas, Departamento de Álgebra, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012 Sevilla, Spain (fmuro@us.es), http://personal.us.es/fmuro
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Abstract

We develop a theory of minimal models for algebras over a Koszul operad with trivial differential defined over a commutative ring (containing $\mathbb {Q}$ in the symmetric case), not necessarily a field, extending and supplementing the work of Sagave for the associative case. Our minimal models are bigraded and contain a projective resolution of the homology.

Keywords

Operadalgebracohomologyformalityminimal modelresolution

MSC classification

Primary: 55U35: Abstract and axiomatic homotopy theory
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 153 , Issue 4 , August 2023 , pp. 1198 - 1243
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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