English

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.

Keywords

Cite

@article{arxiv.1801.06943,
  title  = {Strictly unital A-infinity algebras},
  author = {Jesse Burke},
  journal= {arXiv preprint arXiv:1801.06943},
  year   = {2018}
}
R2 v1 2026-06-22T23:51:31.121Z