) I am attending a Foundation Course in Representation Theory and I am struggling with the following problem: determine the center of the path algebra KQ for a quiver Q.
First of all I've thought that all the paths in the center must be either trivial paths (one per each vertex) or cycles (starting and ending in the same vertex, otherwise we multiply by trivial paths of length 0 from left/right and we get the path itself and 0, hence contradiction). Moreover, we must take into account only for vertices with no more arrows (paths) leaving/entrying, right? I am a little bit messed up with the problem, any hint would be really appreciated.
Thank you so much in advance!