Abstract
If A is a finite dimensional, connected, hereditary wild k-algebra, k algebraically closed and T a tilting module without preinjective direct summands, then the preprojective componentP of the tilted algebra B=EndA (T) is the preprojective component of a concealed wild factoralgebra C of B. Our first result is, that the growth number ρ(C) of C is always bigger or equal to the growth number ρ(A). Moreover the growth number ρ(C) can be arbitrarily large; more precise: if A has at least 3 simple modules and N is any positive integer, then there exists a natural number n>N such that C is the Kronecker-algebraK n, that is the path-algebra of the quiver
(n arrows).
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Kerner, O. Preprojective components of wild tilted algebras. Manuscripta Math 61, 429–445 (1988). https://doi.org/10.1007/BF01258598
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DOI: https://doi.org/10.1007/BF01258598