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 Auslander (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.

References

• Auslander, Maurice (1974), "Representation theory of Artin algebras. II", Communications in Algebra, 1 (4): 269–310, doi:10.1080/00927877409412807, ISSN 0092-7872, MR 0349747