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# Homology, Homotopy and Applications

## Volume 14 (2012)

### Number 1

### Potentials of homotopy cyclic A-infinity algebras

Pages: 203 – 220

DOI: http://dx.doi.org/10.4310/HHA.2012.v14.n1.a10

#### Authors

#### Abstract

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

#### Keywords

A-infinity algebra, cyclic inner product, potential

#### 2010 Mathematics Subject Classification

46Cxx, 53Dxx