Journal article
TREE NORMAL FORMS FOR QUIVER REPRESENTATIONS
Documenta mathematica Journal der Deutschen Mathematiker-Vereinigung., Vol.24, pp.1245-1294
01/01/2019
DOI: 10.25537/dm.2019v24.1245-1294
Abstract
We explore methods for constructing normal forms of indecomposable quiver representations. The first part of the paper develops homological tools for recursively constructing families of indecomposable representations from indecomposables of smaller dimension vector. This is then specialized to the situation of tree modules, where the existence of a special basis simplifies computations and gives nicer normal forms. Motivated by a conjecture of Kac, we use this to construct cells of indecomposable representations as deformations of tree modules. The second part of the paper develops geometric tools for constructing cells of indecomposable representations from torus actions on moduli spaces of representations. As an application, we combine these methods to construct families of indecomposables grouped into cells. These actually give a normal form for all indecomposables of certain roots.
Details
- Title: Subtitle
- TREE NORMAL FORMS FOR QUIVER REPRESENTATIONS
- Creators
- Ryan Kinser - Univ Iowa, Dept Math, Iowa City, IA 52242 USAThorsten Weist - Berg Univ Wuppertal, Fak Math & Nat Wissensch, Gaussstr 20, D-42097 Wuppertal, Germany
- Resource Type
- Journal article
- Publication Details
- Documenta mathematica Journal der Deutschen Mathematiker-Vereinigung., Vol.24, pp.1245-1294
- DOI
- 10.25537/dm.2019v24.1245-1294
- ISSN
- 1431-0643
- eISSN
- 1431-0643
- Publisher
- FIZ KARLSRUHE-LEIBNIZ-INST INFORMATIONSINFRASTRUKTUR
- Number of pages
- 50
- Language
- English
- Date published
- 01/01/2019
- Academic Unit
- Mathematics
- Record Identifier
- 9984241053102771
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