Let $A = KQ$, where $Q$ is the quiver $$\begin{array}{ccc} & \alpha & \\ 1 & \rightleftarrows & 2 \\ & \beta& \end{array}$$ are there simple right $A$-modules with dimension $\geq3$?
In generally, how to find all simple modules for the given path algebra, especially the infinitely dimensional case?