nLab A-infinity-module

Idea

$A_\infty$-module $M$ over an $A_\infty$-algebra $A$ is an object with an $\infty$-representation of $A$, modelled in the same formalism as the $A_\infty$-algebras are (usually in $k$-linear context, most often in (∞,1)-categories of chain complexes). In particular, one considers $A_\infty$-modules over an associative algebra or a dg-algebra viewed as a special case of an $A_\infty$-algebra.

Definition

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Literature

• Bernhard Keller, Introduction to A-infinity algebras and modules, Homology Homotopy Appl. 3(1) (2001) 1–35 arXiv:math.RA/9910179 addendum.dvi
• Bernhard Keller, Bimodule complexes via strong homotopy actions, Algebr. Represent. Theory 3(4) (2000) 357–376
• Yuri Berest, Oleg Chalykh, $A_\infty$-modules and Calogero-Moser spaces, J. Reine Angew. Math. 607 (2007) 69–112 MR2009f:16019 doi

category: algebra