THE HOMOLOGY OF DIGRAPHS AS A GENERALIZATION OF HOCHSCHILD HOMOLOGY

TURNER, PAUL; WAGNER, EMMANUEL

doi:10.1142/s0219498811005555

Back

Journal article

THE HOMOLOGY OF DIGRAPHS AS A GENERALIZATION OF HOCHSCHILD HOMOLOGY

TURNER, PAUL Département de Mathématiques, Université de Fribourg, CH-1700 Fribourg, Switzerland and Section de Mathématiques, Université de Genève, 1211, Switzerland
WAGNER, EMMANUEL Institut de Mathématiques de Bourgogne, Université de Bourgogne, UMR 5584 du CNRS, BP47870, 21078 Dijon Cedex, France

2012-5-5

Published in:

Journal of Algebra and Its Applications. - World Scientific Pub Co Pte Lt. - 2012, vol. 11, no. 02, p. 1250031

English 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.

Language