导出范畴的n-黏合及上(下)黏合

n-Recollements and upper recollements of derived module categories

本文将Artin代数的无界导出范畴的1-黏合和2-黏合用其子范畴的上(下)黏合来刻画.作为应用,本文阐明了导出范畴的上(下)黏合与代数的整体维数(有限维数)的有限性之间的关系,这推广了Yin和Gao (2016)的结果.设A、B和C均为域k上的代数,且DA有一个关于DB和DC的3-黏合,本文证明了A是有限维的当且仅当B和C也如此.

For Artin algebras, we characterize 1-recollements and 2-recollements of their unbounded derived categories in terms of upper(respectively lower) recollements of certain subcategories. As a result, we clarify the relationship between upper(respectively lower) recollements of derived categories and the finiteness of global(respectively finiteness) dimension of algebras, which generalizes a result of Yin and Gao(2016). Let A, B,and C be algebras over a field k, and DA admit a 3-recollement relative to DB and DC. We prove that A is finite-dimensional if and only if so are B and C.