粘合与弱总体维数的一些注记  

Some Notes on the Recollements and Weak Global Dimension

作　　者：胡永刚 姚海楼[1] HU Yonggang;YAO Hailou(College of Applied Sciences,Beijing University of Technology,Beijing 100124,China)

机构地区：[1]北京工业大学应用数理学院,北京100124

出　　处：《北京工业大学学报》2018年第11期1454-1458,共5页Journal of Beijing University of Technology

基　　金：国家自然科学基金资助项目(11671126)

摘　　要：为研究同调维数,可以利用导出范畴的粘合理论来研究代数的弱总体维数的有限性.假设(D(Mod B),D(Mod A),D(Mod C))是导出范畴的标准粘合.证明标准粘合在满足一定条件下,代数A的弱总体维数有限,当且仅当代数B与C的弱总体维数有限.作为应用,证明弱总体维数的有限性是一种导出等价下的不变量.To study homological dimensions,the finiteness of the weak global dimension of algebras was investigated by the theory of recollements. Assume that（ D（ Mod B）,D（ Mod A）,D（ Mod C）） is a standard recollement of derived categories. Results show that if the standard recollements satisfy some conditions,then the weak global dimension of the algebra A is finite if and only if so are the algebras B and C. As an application,results show that the finiteness of the weak global dimension of an algebra is invariant under derived equivalent.

关 键 词：粘合 导出范畴 弱总体维数 导出等价 

分 类 号：O154.1[理学—数学] O154.2[理学—基础数学]