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math.RT2022
Lattice structure in cluster algebra of finite type and non-simply-laced Ingalls-Thomas bijection
Yasuaki Gyoda
In this paper, we demonstrate that the lattice structure of a set of clusters in a cluster algebra of finite type is anti-isomorphic to the torsion lattice of a certain Geiss-Lecle…
math.RT2021★ 1 cited
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…
math.RT2021
Positive cluster complexes and -tilting simplicial complexes of cluster-tilted algebras of finite type
Yasuaki Gyoda
In this study, we consider the positive cluster complex, a full subcomplex of a cluster complex the vertices of which are all non-initial cluster variables. In particular, we provi…