Infinity-Inner-Products on A-Infinity-Algebras
Thomas Tradler

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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology
