粘合与弱总体维数的一些注记

Some Notes on the Recollements and Weak Global Dimension

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.