Absolutely Koszul algebras and the Backelin-Roos property

TL;DR

This paper investigates absolutely Koszul algebras and those with the Backelin-Roos property, identifying specific Veronese subrings with this property and proving that monomial universally Koszul rings possess it.

Contribution

It characterizes classes of Koszul algebras with the Backelin-Roos property and conjectures a complete classification of certain Veronese subrings.

Findings

Identified Veronese subrings with the Backelin-Roos property

Proved monomial universally Koszul rings have the Backelin-Roos property

Conjectured completeness of the list of such Veronese subrings

Abstract

We study absolutely Koszul algebras, Koszul algebras with the Backelin-Roos property and their behavior under standard algebraic operations. In particular, we identify some Veronese subrings of polynomial rings that have the Backelin-Roos property and conjecture that the list is indeed complete. Among other things, we prove that every universally Koszul ring defined by monomials has the Backelin-Roos property.