Koszul property of a class of graded algebras with nonpure resolutions

Abstract

Given any integers a, b, c, and d with a>1, c≥0, b≥a + c, and d≥b + c, the notion of (a, b, c, d)-Koszul algebra is introduced, which is another class of standard graded algebras with “nonpure” resolutions, and includes many Artin-Schelter regular algebras of low global dimension as specific examples. Some basic properties of (a, b, c, d)-Koszul algebras/modules are given, and several criteria for a standard graded algebra to be (a, b, c, d)- Koszul are provided.

Keywords

Koszul algebras / d-Koszul algebras / Artin-Schelter regular algebras / (abcd)-Koszul algebras / Yoneda algebras

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Higher Education Press and Springer-Verlag Berlin Heidelberg