Potentials of homotopy cyclic $\AI$-algebras

TL;DR

This paper introduces a new potential for homotopy cyclic $ ext{A}_ ext{infinity}$-algebras, extending the concept from cyclic cases and relating it to generalized holonomy maps, with proven properties.

Contribution

It defines and analyzes a novel potential for homotopy cyclic $ ext{A}_ ext{infinity}$-algebras, linking algebraic structures to geometric concepts.

Findings

Defined a potential for homotopy cyclic $ ext{A}_ ext{infinity}$-algebras.

Proved properties of the new potential.

Connected the potential to generalized holonomy maps.

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.