Generalization of Yamagata's theorem on trivial extensions
Let A be a basic, connected finite dimensional algebra over an algebraically closed field K and let T(A) be the trivial extension of A by its minimal injective cogenerator Q. The author strengthens the result of \textit{K. Yamagata} [Lect. Notes Math. 903, 364-371 (1981; Zbl 0475.16016)] that T(A) is representation-infinite if the ordinary quiver of A contains an oriented cycle, by studying the zero-relations in this cycle and using the Galois covering \(\hat A\to T(A)\), where \(\hat A\) is the double infinite matrix algebra generated by A and Q in the sense of \textit{D. Hughes} and \textit{J. Waschbüsch} [Proc. Lond. Math. Soc., III. Ser. 46, 347-364 (1983; Zbl 0488.16021)].
scientific article; zbMATH DE number 4031898
scientific article