Strictly unital A∞-algebras

Given a graded module over a commutative ring, we define a dg-Lie algebra whose Maurer–Cartan elements are the strictly unital A∞-algebra structures on that module. We use this to generalize Positselski's result that a curvature term on the bar construction compensates for a lack of augmentatio...

Full description

Saved in:
Bibliographic Details
Published in:Journal of pure and applied algebra 2018-12, Vol.222 (12), p.4099-4125
Main Author: Burke, Jesse
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Given a graded module over a commutative ring, we define a dg-Lie algebra whose Maurer–Cartan elements are the strictly unital A∞-algebra structures on that module. We use this to generalize Positselski's result that a curvature term on the bar construction compensates for a lack of augmentation, from a field to arbitrary commutative base ring. We also use this to show that the reduced Hochschild cochains control the strictly unital deformation functor. We motivate these results by giving a full development of the deformation theory of a nonunital A∞-algebra.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2018.02.022