The homology of digraphs as a generalisation of Hochschild homology

Turner, Paul ; Wagner, Emmanuel

In: J. Algebra and Its Applications, 2012, vol. 11, no. 2, p. 1250031(13 pages)

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... Plus

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    Summary
    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.