The A-infinity Deformation Theory of a Point and the Derived Categories of Local Calabi-Yaus

Abstract

Let A be an augmented algebra over a semi-simple algebra S. We show that the Ext algebra of S as an A-module, enriched with its natural A-infinity structure, can be used to reconstruct the completion of A at the augmentation ideal. We use this technical result to justify a calculation in the physics literature describing algebras that are derived equivalent to certain non-compact Calabi-Yau three-folds. Since the calculation produces superpotentials for these algebras we also include some discussion of superpotential algebras and their invariants.

arXiv commentFinal version, to be published in J. Algebra

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Cited by in corpus (6)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Donaldson-Thomas theory for Calabi-Yau 4-folds
• Unimodular homotopy algebras and Chern-Simons theory
• Motivic Donaldson-Thomas invariants of the conifold and the refined topological vertex
• Sheaves on local Calabi-Yau varieties
• Hopf algebra actions on differential graded algebras and applications