Infinity-Inner-Products on A-Infinity-Algebras

TL;DR

This paper introduces the concept of infinity-inner-products on A-infinity-algebras, defining related Hochschild cochain complexes and associated graph complexes, advancing the algebraic framework for A-infinity-structures.

Contribution

It defines infinity-inner-products as bimodule maps and constructs a graph complex, providing new tools for studying A-infinity-algebras with inner-products.

Findings

Defined Hochschild cochain complex for A-infinity-algebras

Introduced infinity-inner-product as bimodule map

Constructed associated graph complex

Abstract

In this paper the Hochschild-cochain-complex of an A-infinity-algebra A with values in an A-infinity-bimodule M over A and maps between them is defined. Then, an infinity-inner-product on A is defined to be an A-infinity-bimodule-map between A and its dual A*. There is a graph-complex associated to A-infinity-algebras with infinity-inner-product.