The homology of digraphs as a generalisation of Hochschild homology

Abstract

J. Przytycki has established a connection between the Hochschild homology of an algebra $A$ and the chromatic graph homology of a polygon graph with coefficients in $A$. In general the chromatic graph homology is not defined in the case where the coefficient ring is a non-commutative algebra. In this paper we define a new homology theory for directed graphs which takes coefficients in an arbitrary $A-A$ bimodule, for $A$ possibly non-commutative, which on polygons agrees with Hochschild homology through a range of dimensions.

11 pages, 2 figures

References in corpus (1)

• A categorification for the chromatic polynomial

Cited by in corpus (3)

• Hochschild homology, and a persistent approach via connectivity digraphs
• Combinatorial and Topological Aspects of Path Posets, and Multipath Cohomology
• Multipath cohomology of directed graphs