On the quiver with relations of a repetitive algebra
Let \(A=kQ/(\rho)\) be a finite-dimensional \(k\)-algebra for the quiver \(Q\) with the set of relations \(\rho\) consisting only of zero- or commutativity-relations. The author describes explicitly the quiver of the repetitive algebra [\textit{D. Hughes, J. Waschbüsch}, Proc. Lond. Math. Soc., III. Ser. 46, 347-364 (1983; Zbl 0488.16021)] \(\widehat A\) of \(A\). It is also proved that \(A\) is gentle if and only if \(\widehat A\) is special biserial [\textit{C. M. Ringel}, Bol. Soc. Mat. Mex., III. Ser. 3, No.~2, 235-253 (1997; Zbl 0906.16005)].
scientific article; zbMATH DE number 1333330