The homology of digraphs as a generalisation of Hochschild homology

Details The homology of digraphs as a generalisation of Hochschild homology The homology of digraphs as a generalisation of Hochschild homology

2010-01-29

arxiv.org/abs/1001.5379v1

Mathematics

Geometric Topology

11 pages, 2 figures

Scientific paper

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.

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