Koszul Algebras Associated to Graphs
نویسنده
چکیده
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.
منابع مشابه
Hilbert Series of Algebras Associated to Directed Graphs
In [3] we introduced a new class of algebras A(Γ) associated to layered directed graphs Γ. These algebras arose as generalizations of the algebras Qn (which are related to factorizations of noncommutative polynomials, see [2, 5, 9]), but the new class of algebras seems to be interesting by itself. Various results have been proven for algebras A(Γ). In [3] we constructed a linear basis in A(Γ). ...
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