Correction to Group algebras of finite representation type

Abstract

Recently we have observed that Lemma 4 in [-8] is not true and hence the characterization of group algebras of finite representation type given in [-8] is not complete.Here, we will give the correct version of [-8, Theorem] and we will complete the proof given there.We use the same notation as in E8]. In order to state the main result, we need some additional. Let F be a division algebra over a fixed field K. We will denote by Rr(1 ) the quiver algebra FQ1 (in the sense of [3]) of the quiver QI" 1~2~-3 and by RF(2 ) the opposite algebra to Rv(1 ). Moreover, we will denote by RF (3 ) the bounden quiver algebra FQz/I 2 where Q2 is the quiver ~3 ~2~ =2 3+---4and 12 is the ideal in the quiver algebra FQ2 generated by c%c%, and by Re(4 ) the opposite algebra to RF(3 ). Finally, recall that for nonnegative integers m and n, Rv(m,n ) is the bounden quiver algebra FQ,,,./Im, . where Q,,,, is the quiver quiver 9 m ;, 9 I-+ )e and Ira, . is the ideal in the quiver algebra FQm,, generated by the composed arrows fiifii+ 1, i= 1, ..., m -1, and c~j+ 1 c~j, j = 1 ..... n -1.

Controlled Wild Algebras

“…Otherwise, A must be some A n n 1 ;...; n s or a factor of R 3 or R 4 or their opposites. By [27,Theorem] and [36, Theorem 1], AG must be tame. Now we consider the case Q A Y n .…”