Abstract / Bemerkung
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
quiver; infinite-dimensional modules of finite-dimensional algebras; Kronecker; representation type (tame and wild)
Ringel CM. Tame algebras are wild. Algebra Colloquium. 1999;6(4):473-480.
Ringel, C. M. (1999). Tame algebras are wild. Algebra Colloquium, 6(4), 473-480.
Ringel, C. M. (1999). Tame algebras are wild. Algebra Colloquium 6, 473-480.
Ringel, C.M., 1999. Tame algebras are wild. Algebra Colloquium, 6(4), p 473-480.
C.M. Ringel, “Tame algebras are wild”, Algebra Colloquium, vol. 6, 1999, pp. 473-480.
Ringel, C.M.: Tame algebras are wild. Algebra Colloquium. 6, 473-480 (1999).
Ringel, Claus Michael. “Tame algebras are wild”. Algebra Colloquium 6.4 (1999): 473-480.