Motivated by the concept of a torsion pair in a pre-triangulated category induced by Beligiannis and Reiten, the notion of a left (right) torsion pair in the left (right) triangulated category is introduced and invest...Motivated by the concept of a torsion pair in a pre-triangulated category induced by Beligiannis and Reiten, the notion of a left (right) torsion pair in the left (right) triangulated category is introduced and investigated. We provide new connections between different aspects of torsion pairs in one-sided triangulated categories, pre-triangulated categories, stable categories and derived categories.展开更多
The purpose of this paper is to provide the TTF-theories and investigate the comparisons of recollements(one-sided recollements) both induced by the BB-tilting modules.
This paper investigates the structure of the"missing part"from the category of coherent sheaves over a weighted projective line of weight type(2,2,n)to the category of finitely generated right modules on the...This paper investigates the structure of the"missing part"from the category of coherent sheaves over a weighted projective line of weight type(2,2,n)to the category of finitely generated right modules on the associated canonical algebra.By constructing a t-structure in the stable category of the vector bundle category,we show that the"missing part"is equivalent to the heart of the t-structure,hence it is abelian.Moreover,it is equivalent to the category of finitely generated modules on the path algebra of type An-1.展开更多
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10671161) the Cultivation Fund of the Key Scientific and Technical Innovation Project of Ministry of Education of China (Grant NO. 704004)the Natural Science Foundation of Fujian Province (Grant No.Z0511021)
文摘Motivated by the concept of a torsion pair in a pre-triangulated category induced by Beligiannis and Reiten, the notion of a left (right) torsion pair in the left (right) triangulated category is introduced and investigated. We provide new connections between different aspects of torsion pairs in one-sided triangulated categories, pre-triangulated categories, stable categories and derived categories.
基金supported by National Natural Science Foundation of China(Grant No.10931006)
文摘The purpose of this paper is to provide the TTF-theories and investigate the comparisons of recollements(one-sided recollements) both induced by the BB-tilting modules.
基金supported by National Natural Science Foundation of China(Grant Nos.11201386,10931006,11071040 and 11201388)the Natural Science Foundation of Fujian Province of China(Grant No.2012J05009)
文摘This paper investigates the structure of the"missing part"from the category of coherent sheaves over a weighted projective line of weight type(2,2,n)to the category of finitely generated right modules on the associated canonical algebra.By constructing a t-structure in the stable category of the vector bundle category,we show that the"missing part"is equivalent to the heart of the t-structure,hence it is abelian.Moreover,it is equivalent to the category of finitely generated modules on the path algebra of type An-1.
