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arXiv · 2012.07459

Iyama's higher Auslander correspondence via the homological theory of idempotent ideals

Jordan McMahon
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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.

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BibTeXRIS

Jordan McMahon. 2020-12-14. Iyama's higher Auslander correspondence via the homological theory of idempotent ideals. https://arxiv.org/abs/2012.07459

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