Indecomposable representations of the Kronecker quivers
| Autor: | Claus Michael Ringel |
|---|---|
| Rok vydání: | 2010 |
| Předmět: |
Quaternion algebra
Applied Mathematics General Mathematics Quiver Lambda Filtered algebra Combinatorics symbols.namesake Kronecker delta 16G20 05C05 11B39 15A22 16G60 17B67 65F50 symbols Algebra representation FOS: Mathematics Cellular algebra Representation Theory (math.RT) Indecomposable module Mathematics::Representation Theory Mathematics - Representation Theory Mathematics |
| DOI: | 10.48550/arxiv.1009.5635 |
| Popis: | Let k be a field and Lambda the n-Kronecker algebra. This is the path algebra of the quiver with 2 vertices, a source and a sink, and n arrows from the source to the sink. It is well known that the dimension vectors of the indecomposable Lambda-modules are the positive roots of the corresponding Kac-Moody algebra. Thorsten Weist has shown that for every positive root there are tree modules with this dimension vector and that for every positive imaginary root there are at least n tree modules. Here, we present a short proof of this result. The considerations used also provide a calculation-free proof that all exceptional modules over the path algebra of a finite quiver are tree modules. |
| Databáze: | OpenAIRE |
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