  We introduce the class of dominant Auslander-Gorenstein algebras as a
generalisation of higher Auslander algebras and minimal Auslander-Gorenstein
algebras, and give their basic properties. We also introduce mixed (pre)cluster
tilting modules as a generalisation of (pre)cluster tilting modules, and
establish an Auslander type correspondence by showing that dominant
Auslander-Gorenstein (respectively, Auslander-regular) algebras correspond
bijectively with mixed precluster (respectively, cluster) tilting modules. We
show that every trivial extension algebra $T(A)$ of a $d$-representation-finite
algebra A admits a mixed cluster tilting module and show that this can be seen
as a generalisation of the well known result that $d$-representation-finite
algebras are fractionally Calabi-Yau. We show that iterated SGC-extensions of a
gendo-symmetric dominant Auslander-Gorenstein algebra admit mixed precluster
tilting modules.
