19 citations · 59 across the 17 of their papers we have counts for
17 papers
F-invariant in cluster algebras
Peigen Cao
We consider skew-symmetrizable (upper) cluster algebras with a compatible Poisson structure, called -(upper) cluster algebras. For any two good elements (e.g., cluster mo…
Relative left Bongartz completions and their compatibility with mutations
Peigen Cao, Yu Wang, Houjun Zhang
In this paper, we introduce relative left Bongartz completions for a given basic -rigid pair in the module category of a finite dimensional algebra . They give a fami…
On Leclerc's conjectural cluster structures for open Richardson varieties
Peigen Cao, Bernhard Keller
In 2016, Leclerc constructed conjectural cluster structures on open Richardson varieties using representations of preprojective algebras. A variant with more explicit seeds was obt…
The valuation pairing on an upper cluster algebra
Peigen Cao, Bernhard Keller, Fan Qin
It is known that many (upper) cluster algebras are not unique factorization domains. We exhibit the local factorization properties with respect to any given seed : any non-zero…
On exchange matrices from string diagrams
Peigen Cao
Inspired by Fock-Goncharov's amalgamation procedure \cite{Fock-Goncharov-2006}, Shen-Weng introduced string diagrams in \cite{Shen-Weng-2021}, which are very useful to describe man…
Bongartz completion via -vectors
Peigen Cao, Yasuaki Gyoda, Toshiya Yurikusa
In the present paper, we first give a characterization for Bongartz completion in -tilting theory via -vectors. Motivated by this characterization, we give the definition of…