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THE HOMOLOGY OF DIGRAPHS AS A GENERALIZATION OF HOCHSCHILD HOMOLOGY

2010

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.

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]57M15 16E40 05C20Homology (mathematics)[ MATH.MATH-CO ] Mathematics [math]/Combinatorics [math.CO]Mathematics::Algebraic Topology01 natural sciencesCombinatoricsMathematics - Geometric TopologyMathematics::K-Theory and Homology[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT][MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO][ MATH.MATH-KT ] Mathematics [math]/K-Theory and Homology [math.KT]0103 physical sciencesFOS: MathematicsMathematics - CombinatoricsChromatic scale0101 mathematicsMathematics::Symplectic GeometryMathematicsAlgebra and Number TheoryHochschild homologyApplied Mathematics010102 general mathematicsGeometric Topology (math.GT)K-Theory and Homology (math.KT)Directed graphMathematics::Geometric TopologyGraphMathematics - K-Theory and HomologyPolygon[MATH.MATH-KT]Mathematics [math]/K-Theory and Homology [math.KT]BimoduleCombinatorics (math.CO)010307 mathematical physicsJournal of Algebra and Its Applications
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