Tame algebras are wild
We consider the quivers K(n) with two vertices a,b and n arrows a --> b; the quiver K(2) is usually called the Kronecker quiver since the finite-dimensional representations of K(2) are just the matrix pencils studied and classified by Kronecker. The quiver K(2) is a typical tame quiver, whereas the quivers K(n) with n greater than or equal to 3 are wild. it has been known that the category of (not necessarily finite-dimensional) representations of the Kronecker quiver K(2) has a full exact abelian subcategory which is equivalent to the category of representations of K(3). Here, we are going to present a short direct proof
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Springer Verlag