Cluster Algebras and Maximal Green Sequences for Closed Surfaces

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. In this paper we will provide a triangulation for orientable surfaces of genus n with an arbitrary number interior marked points (called punctures) whose corresponding quiver has a maximal green sequence.

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Applied Mathematics

Grantor

Mathematics

Year dc:date.available

2016

Author dc:creator

• Bucher, Eric

• cluster algebras
• maximal green sequences
• algebra
• representation theory
• cluster
• Eric Bucher
• mathematics
• surface
• torus

Statement dc:rights

• unrestricted
• Release the entire work immediately for access worldwide.

Identifier

etd-07052016-180347
https://repository.lsu.edu/gradschool_dissertations/205

OAI identifier oai:identifier

oai:repository.lsu.edu:gradschool_dissertations-1204