Unfoldings and APR-tilts
Let \(A\) be a finite dimensional, basic, connected, associative algebra with an identity over an algebraically closed field, and whose ordinary quiver has no oriented cycles. The authors give an effective criterion for determining whether or not \(A\) is iterated tilted of euclidean type or tilting-cotilting equivalent to a tubular canonical algebra. If \(A\) is representation-infinite, this problem is solved by \textit{I. Assem} and \textit{A. Skowroński} [in Math. Ann. 280, 441-463 (1988; Zbl 0617.16017)]. The presented algorithm is equivalent to that introduced by \textit{S. Brenner} [Proc. Lond. Math. Soc., III. Ser. 62, 242-274 (1991; Zbl 0679.16015)] and uses an unfolding tower of full additive subcategories of the homotopy category \(K^ b({\mathcal P}_ A)\) of bounded complexes of projective \(A\)-modules.
finite dimensional, basic, connected, associative algebra
tilting-cotilting equivalent to a tubular canonical algebra
scientific article; zbMATH DE number 579542