𝑛-representation-finite algebras and 𝑛-APR tilting

Iyama, Osamu; Oppermann, Steffen

doi:10.1090/S0002-9947-2011-05312-2

$n$-representation-finite algebras and $n$-APR tilting
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Trans. Amer. Math. Soc. 363 (2011), 6575-6614 Request permission

Abstract:

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 “type A”.

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