Quiver algebras have the property that, in any fixed dim, rep(Q) is a vector space. Is there some characterization of which algebras have this property?

(Unital algebras seem to be ruled out. Except kQ *is* unital, but for those you can just "throw away" the 1, and all the primitive idempotents in fact, and it works. I guess it's because they have an k-linear decomposition \(kQ = E \oplus I\) where E is the subalgebra of idempotents and I is an ideal, and any representation of Q is uniquely determined by what it does on I (which is a non-unital subalgebra), since it has no choice of what to do on E. Not quite sure what the right general principle is here though...)

#RepresentationTheory #quivers

Anyone know the tame/wild classification for finite *cyclic* quivers? The oft-quoted one is for acyclic.

I can see any quiver w/ two cycles is wild, and any graph that is just one cycle is tame. Having trouble finding anything written about classifying other unicyclic quivers.

#RepresentationTheory #quivers #wild