数学物理学报 ›› 2011, Vol. 31 ›› Issue (2): 394-400.

• 论文 • 上一篇    下一篇

分段Koszul -型代数

吕家凤, 陈淼森   

  1. 浙江师范大学数学系 |浙江 金华 321004
  • 收稿日期:2008-08-07 修回日期:2009-10-28 出版日期:2011-04-25 发布日期:2011-04-25
  • 基金资助:

    浙江省创新计划(T200905)资助

Piecewise-Koszul-Type Algebras

 LV Jia-Feng, CHEN Miao-Sen   

  1. Department of Mathematics, Zhejiang Normal University, Zhejiang Jinhua 321004
  • Received:2008-08-07 Revised:2009-10-28 Online:2011-04-25 Published:2011-04-25
  • Supported by:

    浙江省创新计划(T200905)资助

摘要:

该文引入了分段Koszul -型代数, 它是一类包含某些整体维数是5的AS -正则代数的齐次代数. 文中用极小分次自由解和广义Castelnuovo-Mumford 正则性刻画了这类代数. 讨论了分段Koszul -型代数的Yoneda代数$\bigoplus\limits_{i\geq0}{\rm Ext}_A^i({\Bbb K},{\Bbb K})$
的结构和性质. 特别地, 通过Yoneda代数的生成次数, 给出了一个分次代数是分段Koszul -型代数的充分必要条件.

关键词: 分段Koszul -型代数, Yoneda 代数

Abstract:

Piecewise-Koszul-type algebras, including some Artin-Schelter regular algebras of global dimension five, are introduced in this
paper. It is showed  that the `piecewise-Koszul-type property' of an algebra can be characterized by its minimal graded free resolution
and the associated generalized Castelnuovo-Mumford regularity. The structure of the Yoneda algebra $\bigoplus\limits_{i\geq0}{\rm Ext}_A^i({\Bbb K},{\Bbb K})$ of a piecewise-Koszul-type algebra is investigated. In particular, a necessary and sufficient condition for a graded algebra to be piecewise-Koszul-type is given in terms of the Yoneda algebra.

Key words: Piecewise-Koszul-type algebras, Yoneda algebras

中图分类号: 

  • 16E05