Recollements, Tilting Homological Dimensions and Higher-Dimensional Auslander-Reiten Theory
Received:January 16, 2019  Revised:October 29, 2019
Key Word: recollement   tilting homological dimension   $n$-almost split sequence  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11671126).
Author NameAffiliation
Xuerong FU College of Mathematics and Statistics, Heze University, Shandong 274015, P. R. China 
Hailou YAO College of Applied Sciences, Beijing University of Technology, Beijing 100124, P. R. China 
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      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 $(\mathscr{A}, \mathscr{B}, \mathscr{C})$.
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