Invariance of selfinjective algebras of quasitilted type under stable equivalences. (Q818808)

This paper provides the final step in proving that the class of self-injective algebras of quasi-tilted type is closed under stable or derived equivalences. By a major result of \textit{D. Happel} [Invent. Math. 144, No. 2, 381-398 (2001; Zbl 1015.18006)], quasi-tilted algebras are either of tilted type or of canonical type. Passing to their repetitive algebras and then taking quotients modulo admissible automorphisms, one obtains the self-injective algebras of quasi-tilted type, which again are either of tilted or of canonical type. \textit{A. Skowroński} and \textit{K. Yamagata} have already shown [in Proc. Am. Math. Soc. 132, No. 3, 659-667 (2004; Zbl 1065.16016) and in Algebr. Represent. Theory 9, No. 1, 33-45 (2006; Zbl 1119.16010)] the stable and derived invariance of self-injective algebras of tilted type. The paper under review settles the remaining case of canonical type, by a detailed analysis of the representation theory of these algebras.