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arXiv · 1612.09141

The elementary 3-Kronecker modules

Claus Michael Ringel
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Abstract

The 3-Kronecker quiver has two vertices, namely a sink and a source, and 3 arrows. A regular representation of a representation-infinite quiver such as the 3-Kronecker quiver is said to be elementary provided it is non-zero and not a proper extension of two regular representations. Of course, any regular representation has a filtration whose factors are elementary, thus the elementary representations may be considered as the building blocks for obtaining all the regular representations. We are going to determine the elementary $3$-Kronecker modules. It turns out that all the elementary modules are combinatorially defined.

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Claus Michael Ringel. 2016-12-29. The elementary 3-Kronecker modules. https://arxiv.org/abs/1612.09141

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