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Maximal Green Sequences for Cluster Algebras Associated to Orientable Surfaces with Empty Boundary

Maximal Green Sequences for Cluster Algebras Associated to Orientable Surfaces with Empty Boundary Given a marked surface (S, M) we can add arcs to the surface to create a triangulation, T, of that surface. For each triangulation, T, we can associate a cluster algebra. In this paper we will consider orientable surfaces of genus n with two interior marked points and no boundary component. We will construct a specific triangulation of this surface which yields a quiver. Then in the sense of work by Keller we will produce a maximal green sequence for this quiver. Since all finite mutation type cluster algebras can be associated to a surface, with some rare exceptions, this work along with previous work by others seeks to establish a base case in answering the question of whether a given finite mutation type cluster algebra exhibits a maximal green sequence. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Arnold Mathematical Journal Springer Journals

Maximal Green Sequences for Cluster Algebras Associated to Orientable Surfaces with Empty Boundary

Arnold Mathematical Journal , Volume 2 (4) – Sep 29, 2016

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References (8)

Publisher
Springer Journals
Copyright
Copyright © 2016 by Institute for Mathematical Sciences (IMS), Stony Brook University, NY
Subject
Mathematics; Mathematics, general
ISSN
2199-6792
eISSN
2199-6806
DOI
10.1007/s40598-016-0057-3
Publisher site
See Article on Publisher Site

Abstract

Given a marked surface (S, M) we can add arcs to the surface to create a triangulation, T, of that surface. For each triangulation, T, we can associate a cluster algebra. In this paper we will consider orientable surfaces of genus n with two interior marked points and no boundary component. We will construct a specific triangulation of this surface which yields a quiver. Then in the sense of work by Keller we will produce a maximal green sequence for this quiver. Since all finite mutation type cluster algebras can be associated to a surface, with some rare exceptions, this work along with previous work by others seeks to establish a base case in answering the question of whether a given finite mutation type cluster algebra exhibits a maximal green sequence.

Journal

Arnold Mathematical JournalSpringer Journals

Published: Sep 29, 2016

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