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On a class of algebras associated to directed graphs. (English) Zbl 1080.05040

Summary: To any directed graph we associate an algebra with edges of the graph as generators and with relations defined by all pairs of directed paths with the same origin and terminus. Such algebras are related to factorizations of polynomials over noncommutative algebras. We also construct a basis for our algebras associated to layered graphs.

MSC:

05C20 Directed graphs (digraphs), tournaments
15A15 Determinants, permanents, traces, other special matrix functions
16W30 Hopf algebras (associative rings and algebras) (MSC2000)
16S37 Quadratic and Koszul algebras
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