On The Mutations Loops of Valued Quivers
I Saleh - arXiv preprint arXiv:2207.03142, 2022 - arxiv.org
A mutation loop of a valued quiver $ Q $, is a combination of quiver automorphisms
(permutations of vertices and valuations) and mutations that sends $ Q $ to itself. In this …
(permutations of vertices and valuations) and mutations that sends $ Q $ to itself. In this …
Symmetric mutation algebras in the context of subcluster algebras
I Saleh - Journal of Algebra and Its Applications, 2024 - World Scientific
For a rooted cluster algebra 𝒜 (Q) over a valued quiver Q, a symmetric cluster variable is any
cluster variable belonging to a cluster associated with a quiver σ (Q), for some permutation …
cluster variable belonging to a cluster associated with a quiver σ (Q), for some permutation …
Rooted mutation groups and finite type cluster algebras
I Saleh - arXiv preprint arXiv:2402.17027, 2024 - arxiv.org
For a fixed seed $(X, Q) $, a\emph {rooted mutation loop} is a sequence of mutations that
preserves $(X, Q) $. The group generated by all rooted mutation loops is called\emph …
preserves $(X, Q) $. The group generated by all rooted mutation loops is called\emph …