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Stability Conditions for Affine Type A

  • P. J. Apruzzese
  • Kiyoshi IgusaEmail author
Open Access
Article
  • 22 Downloads

Abstract

We construct maximal green sequences of maximal length for any affine quiver of type A. We determine which sets of modules (equivalently c-vectors) can occur in such sequences and, among these, which are given by a linear stability condition (also called a central charge). There is always at least one such maximal set which is linear. The proofs use representation theory and three kinds of diagrams shown in Fig. 1. Background material is reviewed with details presented in two separate papers Igusa (2017a, b).

Keywords

Maximal green sequences Cluster mutation Quivers c-vectors Central charge Wire diagram Wall crossing 

Mathematics Subject Classification (2010)

16G20 

Notes

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© The Author(s) 2019

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ConnecticutStorrsUSA
  2. 2.Department of MathematicsBrandeis UniversityWalthamUSA

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