The Algebra K₃ is Koszul

2005/11/23 by Nacin, David
#16S37 #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.math/0511589

Abstract

The algebras Q_n describe the relationship between the roots and coefficients of a non-commutative polynomial. I.Gelfand, S.Gelfand, and V. Retakh have defined quotients of these algebras corresponding to graphs. In this work we find the Hilbert series of the class of algebras corresponding to the graph K₃. We also show this algebra is Koszul using the lattice definition.

Related

• The Algebra P_n is Koszul
• Algebras associated to pseudo-roots of noncommutative polynomials are Koszul
• Construction of some algebras associated to directed graphs and related to factorizations of noncommutative polynomials
• Koszul algebras associated to graphs
• The Minimal Non-Koszul A(Gamma)