Recollements, tilting homological dimensions and higher-dimensional Auslander-Reiten theory
Received:January 16, 2019  Revised:May 14, 2019
Key Word: Recollement, the tilting homological dimension, n-almost split sequence.  
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Author NameAffiliationE-mail
Xuerong Fu College of Mathematics and Statistics, Heze University xuerongfu.0098@163.com 
Hailou Yao Beijing University of Technology  
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Abstract:
      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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