Relative homological dimensions in recollements of triangulated categories  

作　　者：Yonggang HU Hailou YAO 

机构地区：[1]College of Applied Sciences, Beijing University of Technology, Beijing 100124, China

出　　处：《Frontiers of Mathematics in China》2019年第1期25-43,共19页中国高等学校学术文摘·数学（英文）

基　　金：National Natural Science Foundation of China (Grant No. 11671126).

摘　　要：Let E be a proper class of triangles in a triangulated category C, and let (A, B, C) be a recollement of triangulated categories. Based on Beligiannis's work, we prove that A and C have enough E-projective objects whenever B does. Moreover, in this paper, we give the bounds for the E-global dimension of B in a recollement (A, B, C) by controlling the behavior of the E-global dimensions of the triangulated categories A and C: In particular, we show that the finiteness of the E-global dimensions of triangulated categories is invariant with respect to the recollements of triangulated categories.

关 键 词：Triangula ted CATEGORY PROPER class of TRIANGLES RECOLLEMENT Sglobal DIMENSION derived CATEGORY 

分 类 号：O[理学]