Auslander algebra

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In mathematics, the Auslander algebra of an algebra A is the endomorphism ring of the sum of the indecomposable modules of A. It was introduced by {{harvs|txt|authorlink=Maurice Auslander|last=Auslander|year=1974}}.

An Artin algebra Γ is called an Auslander algebra if gl dim Γ ≤ 2 and if 0 → Γ → I → J → K → 0 is a minimal injective resolution of Γ then I and J are projective Γ-modules.