| 毛雪峰.连通微分分次代数的整体维数[J].数学年刊A辑,2009,30(3):359~376 |
| 连通微分分次代数的整体维数 |
| Global Dimension for Connected Differential Graded Algebras |
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| DOI： |
| 中文关键词: 连通微分分次代数 微分分次代数 正则微分分次代数 整体维数 紧对象 锥长度 |
| 英文关键词:Connected graded algebra, Differential graded algebra, Regular
DG algebra, Global dimension, Compact object, Cone length |
| 基金项目: |
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| 中文摘要: |
| 首次把有理同伦论中的同伦不变量-锥长度(cone length)引入到微分分次(简记为DG)同调代数中,定义了连通DG代数上DG模的锥长度.连通DG代数A的左(右)整体维数定义为所有DGA-模(Aop-模)的锥长度的上确界.在一些特殊情形下,发现连通.DG代数A的左(右)整体维数与H(A)的整体维数有着密切的关系.任意一个连通分次代数,如果将它视为微分为O的连通DG代数,其左(右)整体维数与其作为连通分次代数的整体维数是一致的.因此该定义是连通分次代数整体维数的一种推广形式.证明A的整体维数足三角范畴D(A)以及Dc(A)的维数的一个上界.当A是正则DG代数时,给出了A的左(右)整体维数的一个有限上界. |
| 英文摘要: |
| This paper introduces a new invariant, which is called cone length, for DG
modules over a connected DG algebra A. The supremum of cone lengthes of all DG A-
modules (respectively, DG Aop-modules) is defined to be the left (respectively, right) global
dimension of A, which is a kind of DG generalization of the global dimension of connected
graded algebras. In some cases, the left (right) global dimension of A has a close relation with
the global dimension of H(A). The global dimension of A is proved to be an upper bound
of the dimension of the triangulated categories D(A) and Dc(A). When the connected DG
algebra A is regular, a finite upper bound of the left (respectively, right) global dimension
of A is discovered. |
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