Recollements of Module Categories

We establish a correspondence between recollements of abelian categories up to equivalence and certain TTF-triples. For a module category we show, moreover, a correspondence with idempotent ideals, recovering a theorem of Jans. Furthermore, we show that a recollement whose terms are module categories is equivalent to one induced by an idempotent element, thus answering a question by Kuhn.     

Recollements and tilting objects

We study connections between recollements of the derived category D(Mod R) of a ring R and tilting theory. We first provide constructions of tilting objects from given recollements, recovering several different results from the literature. Secondly, we show how to construct a recollement from a tilting module of projective dimension one. By Nicolás and Saorín (2009) [31], every recollement of D(Mod R) is associated to a differential graded homological epimorphism λ:R→S. We will focus on the case where λ is a homological ring epimorphism or even a universal localization. Our results will be employed in a forthcoming paper in order to investigate stratifications of D(Mod R).     

Recollements of extension algebras

Let A be a finite-dimensional algebra over arbitrary base field k. We prove: if the unbounded derived module category D-(Mod-A) admits symmetric recollement relative to unbounded derived module categories of two finite-dimensional k-algebras B and C:D- (Mod - B) D-(Mod - A) D-(Mod - C),then the unbounded derived module category D-(Mod - T(A)) admits symmetric recollement relative to the unbounded derived module categories of T(B) and T(C):D-(Mod - T(B)) D-(Mod - T(A)) D-(Mod -T(C)).     

Recollements and homological dimensions

We investigate the behavior of the homological dimensions under recollements of derived categories of algebras. In particular, we establish a series of new bounds among the self-injective dimensions or ?-dimensions of the algebras linked by recollements of derived module categories.     

Abel范畴的右双-Giraud粘合

我们在本文中引入了Abel范畴的右双-Giraud粘合定义.我们证明了右双-Giraud粘合与余遗传和遗传的挠对存在着双射对应.此外,我们通过模范畴中特定的幂等理想刻画了这类挠对.     

On the Recollements of Functor Categories

This paper is devoted to the study of recollements of functor categories in different levels. In the first part of the paper, we start with a small category \(\mathcal {S}\) and a maximal object s of \(\mathcal {S}\) and construct a recollement of \(\text {Mod-}\mathcal {S}\) in terms of \(\text {Mod-End}_{\mathcal {S}}(s)\) and \(\text {Mod-}(\mathcal {S}\setminus \{s\})\) in four different levels. In case \(\mathcal {S}\) is a finite directed category, by iterating this argument, we get chains of recollements having some interesting applications. In the second part, we start with a recollement of rings and construct a recollement of their path rings, with respect to a finite quiver. Third part of the paper presents some applications, including recollements of triangular matrix rings, an example of a recollement in Gorenstein derived level and recollements of derived categories of N-complexes.     

Recollements of Singularity Categories and Monomorphism Categories

We generalize results on existence of recollement situations of singularity categories of lower triangular Gorenstein algebras and stable monomorphism categories of Cohen–Macaulay modules.     

Recollements,idempotent completions and t-structures of triangulated categories

We first prove that the idempotent completion of a right or left recollement of triangulated categories is still a right or left recollement, then show that the t-structure on a triangulated category is compatible with taking idempotent completion. Finally, an application of the main theorem is given, which is focused on the boundedness and nondegeneration of the t-structure induced by a recollement and its idempotent completion.     

Recollements arising from cotorsion pairs on extriangulated categories

This paper is devoted to constructing some recollements of additive categories associated to concentric twin cotorsion pairs on an extriangulated category. As an application, this result generalizes the work by W. J. Chen, Z. K. Liu, and X. Y. Yang in a triangulated case [J. Algebra Appl., 2018, 17(5): 1–15]. Moreover, it highlights new phenomena when it applied to an exact category. Finally, we give some applications of our main results. In particular, we obtain Krause's recollement whose proofs are both elementary and very general.     

正合范畴中的复形、余挠对及粘合

作者在弱幂等完备的正合范畴(A,E)中引入了复形的新的定义,并且证明了E-正合复形的同伦范畴Kex(E)是同伦范畴KE(A)的厚子范畴.给定(A,E)中的余挠对(x,y),定义了正合范畴(CE(A),C(E))中的两个余挠对((x)E,dg(y)E)和(dg(x)E,(y)E),并且证明了当A是可数完备时,CE(A)中...     

Recollements of self-injective algebras,and classification of self-injective diagram algebras

Mathematische Zeitschrift - Diagram algebras, in particular Brauer algebras, Birman–Murakami-Wenzl algebras and partition algebras, are used in representation theory and invariant theory of...     

粘合、倾斜同调维数与高维Auslander-Reiten理论

本文主要研究阿贝尔范畴粘合$(\mathscr{A}, \mathscr{B}, \mathscr{C})$中$\mathscr{A}$, $\mathscr{B}$与$\mathscr{C}$之间的倾斜同调维数关系. 特别地,对遗传的阿贝尔范畴$\mathscr{B}$,给出了粘合$(\mathscr{A}, \mathscr{B}, \mathscr{C})$中的范畴之间的$n$-几乎可裂序列间的联系.     

左非奇异左CS-环和左遗传左CS-环

本文首先证明了：环为左非奇异左CS-环当且仅当它为左余非奇异Baer环,然后给出左遗传左CS-环,正则左遗传左CS-环和左遗传左连续环的某些刻划.     

Comparisons of Block Iterative Methods

Comparison theorems for spectral radii of two block USSOR methods, two block SSOR methods, two block AOR methods, two block SOR methods with respect to a partition and the corresponding finer partition ^* are given, respectively, whenever A is an M-matrix or an H-matrix.     

Comparisons of regular splittings of matrices

Summary In this article, new comparison theorems for regular splittings of matrices are derived. In so doing, the initial results of Varga in 1960 on regular splittings of matrices, and the subsequent unpublished results of Wonicki in 1973 on regular splittings of matrices, will be seen to be special cases of these new comparison theorems.Dedicated to Fritz Bauer on the occasion of his 60th birthdayResearch supported in part by the Air Force Office of Scientific Research, and by the Department of Energy