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We introduce the notion of n-representation-finiteness, generalizing representation-finite hereditary algebras. We establish the procedure of n-APR tilting and show that it preserves n-representation-finiteness. We give some combinatorial description of this procedure and use this to completely describe a class of n-representation-finite algebras called âtype Aâ.
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Iyama et al. (2011) studied this question.
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