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math.RT2025
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…
math.RT2024
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…
math.RT2014
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…