Quotients of Koszul algebras and 2-d-determined algebras

TL;DR

This paper compares two approaches to studying Koszul-like properties of graded algebras with relations in degrees 2 and another degree, providing new conditions for their Yoneda algebras to be generated in minimal degrees.

Contribution

It contrasts two existing methods, answers open questions, and establishes conditions for Yoneda algebra generation in specific degrees.

Findings

Provided conditions for Yoneda algebras to be generated in minimal degrees

Answered two open questions from prior research

Compared different approaches to Koszul-like properties

Abstract

Vatne and Green & Marcos have independently studied the Koszul-like homological properties of graded algebras that have defining relations in degree 2 and exactly one other degree. We contrast these two approaches, answer two questions posed by Green & Marcos, and find conditions that imply the corresponding Yoneda algebras are generated in the lowest possible degrees.