Relative homological dimensions in recollements of triangulated categories

作     者：Yonggang HU Hailou YAO 

作者机构：College of Applied Sciences Beijing University of Technology Beijing 100124 China 

出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)

年 卷 期：2019年第14卷第1期

页      面：25-43页

核心收录：

学科分类：07[理学] 

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

主　　题：Triangula ted category proper class of triangles recollement Sglobal dimension derived category 

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.