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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…
Induced Representations of Hopf Algebras
Ibrahim Saleh
Hopf representation is a module and comodule with a consistency condition that is more general than the consistency condition of Hopf modules. For a Hopf algebra , we construct…
Cluster Structure on Generalized Weyl Algebras
Ibrahim Saleh
We introduce a class of non-commutative algebras that carry a non-commutative (geometric) cluster structure which are generated by identical copies of generalized Weyl algebras. Eq…
Exchange Maps of Cluster Algebras
Ibrahim A Saleh
Every two seeds in a field of fractions together with a symmetric group element gives rise to an automorphism of called an exchange automorphism. For po…