The Cohen-Macaulay Auslander algebras of string algebras

The Cohen-Macaulay Auslander algebra of any string algebra is explicitly constructed in this paper. Furthermore, we show that a class of special string algebras, which are called to be string algebras with G-condition, are representation-finite if and only if their Cohen-Macaulay Auslander algebras are representation-finite. Finally, the self-injective dimension of gentle algebras is characterized using their Cohen-Macaulay Auslander algebras.