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Iyama's higher Auslander correspondence via the homological theory of idempotent ideals (2012.07459v1)
Published 14 Dec 2020 in math.RT
Abstract: A celebrated result in representation theory is that of higher Auslander correspondence. Let $\Lambda$ an Artin algebra and $X$ a $d$-cluster-tilting module. Iyama has shown that the endomorphism ring $\Gamma$ of $X$ is a $d$-Auslander algebra, and moreover this gives a correspondence between $d$-cluster-tilting modules and $d$-Auslander algebras. We present a self-contained and concise proof using the homological theory of idempotent ideals of Auslander--Platzeck--Todorov.