Strictly unital A-infinity algebras

2018/01/22 by Jesse Burke, Burke, Jesse
Mathematics · #FOS: Mathematics #K-Theory and Homology (math.KT) #math.KT

paper · pdf · doi:10.48550/arxiv.1801.06943

arxiv created 2018/01/22 · arxiv updated 2018/01/23

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.

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