2012/04/06 by David Nacin, Nacin, David
Engineering · Mathematics · #16S37 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1204.1534
openalex publication_date 2012/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The algebras A(Γ), where Γ is a directed layered graph, were first constructed by I. Gelfand, S. Serconek, V. Retakh and R. Wilson. These algebras are generalizations of the algebras Qn, which are related to factorizations of non-commutative polynomials. It was conjectured that these algebras were Koszul. In 2008, T.Cassidy and B.Shelton found a counterexample to this claim, a non-Koszul A(Γ) corresponding to a graph Γ with 18 edges and 11 vertices. We produce an example of a directed layered graph Γ with 13 edges and 9 vertices which produces a non-Koszul A(Γ). We also show this is the minimal example with this property.