On the quiver with relations of a repetitive algebra
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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 Â 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 Â and the derived category of A are equivalent.
KeywordsGlobal Dimension Module Category Stable Module Finite Global Dimension Stable Module Category
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