Quotients of Koszul Algebras and 2-d-Determined Algebras

Abstract

Vatne [13] and Green and Marcos [9] 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 and Marcos, and find conditions that imply the corresponding Yoneda algebras are generated in the lowest possible degrees.

Key Words:

• Koszul algebras
• Yoneda algebras
• 2-d-Determined algebras

2010 Mathematics Subject Classification:

• 16S37
• 16E30

ACKNOWLEDGMENTS

The authors would like to thank Andrew Conner for his helpful suggestions.

Notes

In their formulation, Green and Marcos consider quotients of graph algebras. We only consider connected-graded algebras, which suffice to answer the questions in the negative.

Communicated by E. Kirkman.