The quadratic algebras associated with pseudo-roots of noncommutative polynomials are Koszul algebras

Abstract

The roots and pseudo-roots of a noncommutative polynomial satisfy relations given by the noncommutative Vieta Theorem of Gelfand and Retakh. The quadratic algebras Q n are defined by relations modeled on these relations for roots and pseudo-roots. We show that the algebras Q n are Koszul algebras.