Koszul algebras associated to graphs

Details Koszul algebras associated to graphs Koszul algebras associated to graphs

2006-02-15

arxiv.org/abs/math/0602315v1

Mathematics

Rings and Algebras

8 pages

Scientific paper

Quadratic algebras associated to graphs have been introduced by I. Gelfand,
S. Gelfand, and Retakh in connection with decompositions of noncommutative
polynomials. Here we show that, for each graph with rare triangular subgraphs,
the corresponding quadratic algebra is a Koszul domain with global dimension
equal to the number of vertices of the graph.

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