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Strictly unital A-infinity algebras

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 نشر من قبل Jesse Burke
 تاريخ النشر 2018
  مجال البحث
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 تأليف Jesse Burke




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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 Positselskis 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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