We develop the deformation theory of A∞ algebras together with ∞-inner products and identify a differential graded Lie algebra that controls the theory. This generalizes the deformation theories of associative algebras, A∞ algebras, associative algebras with inner products, and A∞ algebras with inner products.
Homology, Homotopy and Applications, Vol. 8 (2006), No. 2, pp.115-131.
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