Abstract
For a cyclic $\AI$-algebra, a potential recording the structure constants can be defined. We define an analogous potential for a homotopy cyclic $\AI$-algebra and prove its properties. On the other hand, we find another different potential for a homotopy cyclic $\AI$-algebra, which is related to the algebraic analogue of generalized holonomy map of Abbaspour, Tradler and Zeinalian.
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