A-infinity algebras, modules and functor categories

2005/10/24 by Bernhard Keller, Keller, Bernhard · 2 citations
Mathematics · #16D90 #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #{18E30

paper · pdf · doi:10.48550/arxiv.math/0510508

openalex publication_date 2005/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this survey, we first present basic facts on A-infinity algebras and modules including their use in describing triangulated categories. Then we describe the Quillen model approach to A-infinity structures following K. Lefevre's thesis. Finally, starting from an idea of V. Lyubashenko's, we give a conceptual construction of A-infinity functor categories using a suitable closed monoidal category of cocategories. In particular, this yields a natural construction of the bialgebra structure on the bar construction of the Hochschild complex of an associative algebra.

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• Differential graded algebras with divided powers and homotopy Lie algebras
• Cyclic brace relation and BV structure on open-closed Hochschild cohomology

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