Abstract

Let $A = kQ/\langle \rho \rangle $ be a finite-dimensional k-algebra where $\rho $ is a set of relations for the quiver Q. Assume that $\rho $ contains only zero-relations or commutativity-relations. We describe explicitly the quiver with relations of the repetitive algebra  of A. The following well known result of D. Happel is one of the main reasons for studying Â: If A is of finite global dimension, then the stable module category of  and the derived category of A are equivalent.

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