12 citations · 37 across the 21 of their papers we have counts for
18 papers · 1 filter
Tilting mutation of gentle algebras and its combinatorial description
Difan Deng, Shengfei Geng, Pin Liu
Tilting mutation provides a natural way to construct derived-equivalent algebras by replacing an indecomposable summand of a tilting object. Holm, Schröer and Zimmermann~\cite{HSZ0…
Geometric models for endomorphism algebras of tilting modules over gentle algebras
Difan Deng, Shengfei Geng, Pin Liu
This paper investigates tilting modules over gentle algebras and their endomorphism algebras within the framework of marked surfaces and tilings introduced by Baur and Simões. Fait…
Intersection vectors over skew-tilings
Difan Deng, Shengfei Geng, Pin Liu
We prove that under a mild condition, a multiset of tagged permissible arcs over a skew-tiling is uniquely determined by its intersection vector. As an application, it is proved th…
Functor-induced isomorphisms and -matrices
Shengfei Geng
In this paper, we explore how functor-induced isomorphisms are encoded by -matrices. We first show that the Grothendieck group isomorphism induced by a tilting module can be rea…
On denominator conjecture for cluster algebras of finite type
Changjian Fu, Shengfei Geng
We continue our investigation on denominator conjecture of Fomin and Zelevinsky for cluster algebras via geometric models initialed in \cite{FG22}. In this paper, we confirm the de…
Denominator conjecture for some surface cluster algebras
Changjian Fu, Shengfei Geng
The denominator conjecture, proposed by Fomin and Zelevinsky, says that for a cluster algebra, the cluster monomials are uniquely determined by their denominator vectors with respe…
On -tilting graphs for quasi-silted algebras
Wei Dai, Changjian Fu, Shengfei Geng +1
We prove that the -tilting graph of any quasi-silted algebra is connected and has the reachable-in-face property. Our approach utilizes -reduction and wall and chamber struct…
Intersection vectors over tilings with applications to gentle algebras and cluster algebras
Changjian Fu, Shengfei Geng
It is proved that a multiset of permissible arcs over a tiling is uniquely determined by its intersection vector under a mild condition. This generalizes a classical result over ma…
On support -tilting graphs of gentle algebras
Changjian Fu, Shengfei Geng, Pin Liu +1
Let be a finite-dimensional gentle algebra over an algebraically closed field. We investigate the combinatorial properties of support -tilting graph of . In particular, i…
On maximal green sequence for quivers arising from weighted projective lines
Changjian Fu, Shengfei Geng
We investigate the existence and non-existence of maximal green sequences for quivers arising from weighted projective lines. Let be the Gabreil quiver of the endomorphism alge…
On cluster categories of weighted projective lines with at most three weights
Changjian Fu, Shengfei Geng
Let be a weighted projective line and the associated cluster category. It is known that can be realized as a generali…
Relative rigid objects in extriangulated categories
Yu Liu, Panyue Zhou
In this paper, we study a close relationship between relative cluster tilting theory in extriangulated categories and tau-tilting theory in module categories. Our main results show…
Mutation of tilting bundles of tubular type
Shengfei Geng
Let be a weighted projective line of tubular type and the category of coherent sheaves on . The main purpose of this note is…
On cluster-tilting graphs for hereditary categories
Changjian Fu, Shengfei Geng
Let be a connected hereditary abelian category with tilting objects. It is proved that the cluster-tilting graph associated with is always connected. As…
Cluster algebras arising from cluster tubes II: the Caldero-Chapoton map
Changjian Fu, Shengfei Geng, Pin Liu
We continue our investigation on cluster algebras arising from cluster tubes. Let be a cluster tube of rank . For an arbitrary basic maximal rigid object of…
Tilting modules and support -tilting modules over preprojective algebras associated with symmetrizable Cartan matrices
Changjian Fu, Shengfei Geng
For any given symmetrizable Cartan matrix with a symmetrizer , Geiß~ et al. (2016) introduced a generalized preprojective algebra . We study tilting modules and sup…
The singularity categories of the Cluster-tilted algebras of Dynkin type
Xinhong Chen, Shengfei Geng, Ming Lu
In this paper, we use the stable categories of some selfinjective algebras to describe the singularity categories of the cluster-tilted algebras of Dynkin type. Furthermore, in thi…
The Bridgeland's Ringel-Hall algebra associated to an algebra with global dimension at most two
Shengfei Geng, Liangang Peng
For any finitely dimensional associative algebra with global dimension , we show that there is an embedding from the twisted Ringel-Hall algebra to the Brigeland's Ringel-H…