粘合、倾斜同调维数与高维Auslander-Reiten理论

Recollements, Tilting Homological Dimensions and Higher-Dimensional Auslander-Reiten Theory

中文关键词:  粘合  倾斜同调维数  $n$-几乎可裂序列

英文关键词:recollement  tilting homological dimension  $n$-almost split sequence

中文摘要:

      本文主要研究阿贝尔范畴粘合$(\mathscr{A}, \mathscr{B}, \mathscr{C})$中$\mathscr{A}$, $\mathscr{B}$与$\mathscr{C}$之间的倾斜同调维数关系. 特别地,对遗传的阿贝尔范畴$\mathscr{B}$,给出了粘合$(\mathscr{A}, \mathscr{B}, \mathscr{C})$中的范畴之间的$n$-几乎可裂序列间的联系.

英文摘要:

      In this paper we mainly investigate the behavior of tilting homological dimensions of the categories involved in the recollement of abelian categories $(\mathscr{A}, \mathscr{B}, \mathscr{C})$. In particular, when abelian category $\mathscr{B}$ is hereditary, we give the connections between $n$-almost split sequences in the categories of $(\mathscr{A}, \mathscr{B}, \mathscr{C})$.