δ-Koszul Algebras

ABSTRACT

Let A = A ₀  ⊕  A ₁  ⊕  A ₂  ⊕ ··· be a graded K -algebra such that A ₀ is a finite product of copies of the field K, A is generated in degrees 0 and 1,and dim _K A ₁  < ∞. We study those graded algebras A with the property that A ₀ , viewed as a graded A -module, has a graded projective resolution, , such that each P ⁱ can be generated in a single degree. The paper describes necessary and sufficient conditions for the Ext-algebra of A , , to be finitely generated. We also investigate classes of modules over such algebras and Veronese subrings of the Ext-algebra.

Key Words:

• Graded modules and algebras
• Koszul algebras and modules

Mathematics Subject Classification:

• 16G20

ACKNOWLEDGMENTS

The first author was partially support by a grant from the National Security Agency. The second author wants to thank CNPq (Brazil), for financial support, in form of a productivity scholarship.

Notes

^#Communicated by M. Ferrero.