  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.
