Strictly unital A-infinity algebras
K-Theory and Homology
2018-01-23 v1
Abstract
Given a graded module over a commutative ring, we define a dg-Lie algebra whose Maurer-Cartan elements are the strictly unital A-infinity 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-infinity algebra.
Cite
@article{arxiv.1801.06943,
title = {Strictly unital A-infinity algebras},
author = {Jesse Burke},
journal= {arXiv preprint arXiv:1801.06943},
year = {2018}
}