Frontiers of Mathematics in China >

2016 , Vol. 11 >Issue 4: 985 - 1002

DOI: https://doi.org/10.1007/s11464-016-0566-3

RESEARCH ARTICLE

Koszul property of a class of graded algebras with nonpure resolutions

  • Jiafeng LÜ ,
  • Junling ZHENG
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  • Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China

Received date: 21 Jul 2015

Accepted date: 28 Jan 2016

Published date: 30 Aug 2016

Copyright

2016 Higher Education Press and Springer-Verlag Berlin Heidelberg
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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.

Key words： Koszul algebras; d-Koszul algebras; Artin-Schelter regular algebras; (abcd)-Koszul algebras; Yoneda algebras

Cite this article

Jiafeng LÜ , Junling ZHENG . Koszul property of a class of graded algebras with nonpure resolutions[J]. Frontiers of Mathematics in China, 2016 , 11(4) : 985 -1002 . DOI: 10.1007/s11464-016-0566-3

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