2016/12/29 by Ringel, Claus Michael · 1 citation
#FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1612.09141
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.