Algebras associated to pseudo-roots of noncommutative polynomials are Koszul

2004/05/19 by Dmitri Piontkovski
Mathematics · #math.RA #math.QA #msc:16S37 #msc:16W30

paper · pdf

published as Int. J. Algebra Comp., 15(2005), 4, 643-648 · 5 pages

arxiv created 2004/05/19 · arxiv updated 2009/12/01

Abstract

Quadratic algebras associated to pseudo-roots of noncommutative polynomials have been introduced by I. Gelfand, Retakh, and Wilson in connection with studying the decompositions of noncommutative polynomials. Later they (with S. Gelfand and Serconek) shown that the Hilbert series of these algebras and their quadratic duals satisfy the necessary condition for Koszulity. It is proved in this note that these algebras are Koszul.

Related

• Hilbert series of quadratic algebras associated with pseudo-roots of noncommutative polynomials
• The Algebra P_n is Koszul
• The Algebra K₃ is Koszul
• Construction of some algebras associated to directed graphs and related to factorizations of noncommutative polynomials
• Koszul algebras associated to graphs