11 citations · 12 across the 7 of their papers we have counts for
7 papers
Hilbert series of algebras associated to direct graphs and order homology
Vladimir Retakh, Shirlei Serconek, Robert Wilson
We give a homological interpretation of the coefficients of the Hilbert series for an algebra associated with a directed graph and its dual algebra. This allows us to obtain necess…
Koszulity of splitting algebras associated with cell complexes
Vladimir Retakh, Shirlei Serconek, Robert Lee Wilson
We associate to a good cell decomposition of a manifold M a quadratic algebra and show that the Koszulity of the algebra implies a restriction on the Euler characteristic of M. For…
Construction of some algebras associated to directed graphs and related to factorizations of noncommutative polynomials
Vladimir Retakh, Shirlei Serconek, Robert Lee Wilson
This is a survey of recently published results. We introduce and study a wide class algebras associated to directed graphs and related to factorizations of noncommutative polynomia…
Hilbert series of algebras associated to directed graphs
Vladimir Retakh, Shirlei Serconek, Robert Lee Wilson
Few changes. We compute the Hilbert series of some algebras associated to directed graphs and related to factorizations of noncommutative polynomials.
On a class of Koszul algebras associated to directed graphs
Vladimir Retakh, Shirlei Serconek, Robert Lee Wilson
In math.QA/0506507 I. Gelfand and the authors introduced and studied a new class of algebras associated to directed graphs. In this paper we show that these algebras are Koszul for…
On a class of algebras associated to directed graphs
Israel Gelfand, Vladimir Retakh, Shirlei Serconek +1
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. Suc…