5 papers
On the Mutations of Gentle Quivers and Admissible Ideals
Ibrahim Saleh
Fomin Zelevinsky quiver mutation is an essential tool in the theory of cluster algebras. In this paper, we extend this framework to quivers with relations by introducing an involut…
Rooted mutation groups and finite type cluster algebras
Ibrahim Saleh
For a fixed seed , a \emph{rooted mutation loop} is a sequence of mutations that preserves . The group generated by all rooted mutation loops is called \emph{rooted…
On The Mutations Loops of Valued Quivers
Ibrahim Saleh
A mutation loop of a valued quiver , is a combination of quiver automorphisms (permutations of vertices and valuations) and mutations that sends to itself. In this article w…
Symmetric mutations algebras in the context of sub-cluster algebras
Ibrahim Saleh
For a rooted cluster algebra over a valued quiver , a \emph{symmetric cluster variable} is any cluster variable belonging to a cluster associated with a quiver…
Clustered Hyperbolic Categories
Ibrahim Saleh
We introduce a class of categories, called \emph{clustered hyperbolic categories}, which are generated by equivalent categories of representations of some Weyl cluster algebras. Ev…