Construction of some algebras associated to directed graphs and related to factorizations of noncommutative polynomials

2006/03/14 by Vladimir Retakh, Retakh, Vladimir, Shirlei Serconek +3
Engineering · Mathematics · #05E05 #15A15 #16W30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Rings and Algebras (math.RA) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.math/0603327

openalex publication_date 2006/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 polynomials. In particular, we show that for many well-known graphs such algebras are Koszul and compute their Hilbert series.

Related

• Hilbert series of algebras associated to directed graphs
• On a class of algebras associated to directed graphs
• Noncommutative algebras associated to complexes and graphs
• The Algebra K₃ is Koszul
• The Algebra P_n is Koszul