37 citations · 156 across the 27 of their papers we have counts for
25 papers · 1 filter
Derived equivalences for mirror-reflective algebras
Hongxing Chen, Changchang Xi
We show that the construction of mirror-reflective algebras inherits derived equivalences of gendo-symmetric algebras. More precisely, suppose A and B are gendo-symmetric algebras…
Mirror-reflective algebras and Tachikawa's second conjecture
Hongxing Chen, Ming Fang, Changchang Xi
Given an algebra with an idempotent, we introduce two procedures to construct families of new algebras, termed mirror-reflective algebras and reduced mirror-reflective algebras. We…
New invariants of stable equivalences of algebras
Changchang Xi, Jinbi Zhang
We show that stable equivalences between Artin algebras without nodes preserve homological data that provide upper bounds for finitistic dimension, and that stable equivalences bet…
Gorenstein projective modules over rings of Morita contexts
Qianqian Guo, Changchang Xi
Under semi-weak and weak compatibility of bimodules, we establish sufficient and necessary conditions of Gorenstein-projective modules over rings of Morita contexts with one bimodu…
Symmetric subcategories, tilting modules and derived recollements
Hongxing Chen, Changchang Xi
For any good tilting module over a ring , there exists an -symmetric subcategory of a module category such that the derived category of the endomorphism rin…
Invariant algebras of matrices and symmetric polynomials of partitions
Changchang Xi, Jinbi Zhang
For a field of characteristic and a matrix in the full matrix algebra over , let be the centralizer algebra of in .…
Representation dimensions linked by Frobenius bimodules with applications to group algebras
Changchang Xi
We establish relations between representation dimensions of two algebras connected by a Frobenius bimodule or extension. Consequently, upper bounds and equality formulas for repres…
Frobenius bimodules and flat-dominant dimensions
Changchang Xi
We establish relations between Frobenius parts and between flat-dominant dimensions of algebras linked by Frobenius bimodules. This is motivated by the Nakayama conjecture and an a…
Derived decompositions of abelian categories I
Hongxing Chen, Changchang Xi
Derived decompositions of abelian categories are introduced in internal terms of abelian subcategories to construct semi-orthogonal decompositions (or Bousfield localizations, or h…
An application of Nakayama functor in representation stability theory
Wee Liang Gan, Liping Li, Changchang Xi
Using the Nakayama functor, we construct an equivalence from a Serre quotient category of a category of finitely generated modules to a category of finite-dimensional modules. We t…
Milnor squares of algebras, I: derived equivalences
Wei Hu, Changchang Xi
Derived equivalences for Artin algebras (and almost -stable derived equivalences for finite-dimensional algebras) are constructed from Milnor squares of algebras. Particularly,…
Finitistic dimension conjecture and radical-power extensions
Chengxi Wang, Changchang Xi
The finitistic dimension conjecture asserts that any finite-dimensional algebra over a field should have finite finitistic dimension. Recently, this conjecture is reduced to studyi…
Dominant dimensions, derived equivalences and tilting modules
Hongxing Chen, Changchang Xi
The Nakayama conjecture states that an algebra of infinite dominant dimension should be self-injective. Motivated by understanding this conjecture in the context of derived categor…
Derived equivalences and stable equivalences of Morita type, II
Wei Hu, Changchang Xi
Motivated by understanding the Broué's abelian defect group conjecture from algebraic point of view, we consider the question of how to lift a stable equivalence of Morita type bet…
Ringel modules and homological subcategories
Hongxing Chen, Changchang Xi
Given a good -tilting module over a ring , let be the endomorphism ring of , it is an open question whether the kernel of the left-derived functor …
Recollements of derived categories I: Exact contexts
Hongxing Chen, Changchang Xi
Recollements were introduced originally by Beilinson, Bernstein and Deligne to study the derived categories of perverse sheaves, and nowadays become very powerful in understanding…
Stratifications of derived categories from tilting modules over tame hereditary algebras
Hongxing Chen, Changchang Xi
In this paper, we consider the endomorphism algebras of infinitely generated tilting modules of the form over tame hereditary -algebras $…
Derived equivalences from cohomological approximations, and mutations of -Yoneda algebras
Wei Hu, Steffen Koenig, Changchang Xi
In this article, a new construction of derived equivalences is given. It relates different endomorphism rings and more generally cohomological endomorphism rings - including higher…
Good tilting modules and recollements of derived module categories
Hongxing Chen, Changchang Xi
Let be an infinitely generated tilting module of projective dimension at most one over an arbitrary associative ring , and let be the endomorphism ring of . In this p…
Inductions and restrictions for stable equivalences of Morita type
Hongxing Chen, Shengyong Pan, Changchang Xi
In this paper, we present two methods, induction and restriction procedures, to construct new stable equivalences of Morita type. Suppose that a stable equivalence of Morita type b…
Derived equivalences for -Auslander-Yoneda algebras
Wei Hu, Changchang Xi
In this paper, we introduce -Auslander-Yoneda algebras in a triangulated category with a parameter set in , and provide a method to construct new derived equivale…
Transfer of stable equivalences of Morita type
Shengyong Pan, Changchang Xi
Let and be finite-dimensional -algebras over a field such that $A/\rad(A)$ and $B/\rad(B)$ are separable. In this note, we consider how to transfer a stable equivale…
Almost -split sequences and derived equivalences
Wei Hu, Changchang Xi
In this paper, we introduce almost -split sequences and establish an elementary but somewhat surprising connection between derived equivalences and Auslander-Reiten sequenc…
Derived equivalences and stable equivalences of Morita type, I
Wei Hu, Changchang Xi
For self-injective algebras, Rickard proved that each derived equivalence induces a stable equivalence of Morita type. For general algebras, it is unknown when a derived equivalenc…