2020/12/14 by Jordan McMahon, McMahon, Jordan
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2012.07459
openalex publication_date 2020/12/14 · openalex created_date 2020/12/21 · openalex updated_date 2026/07/28
A celebrated result in representation theory is that of higher Auslander correspondence. Let Λ an Artin algebra and X a d-cluster-tilting module. Iyama has shown that the endomorphism ring Γ 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.