TITLE: Auslander-Reiten theory for Gorenstein algebras
QUESTION [6 upvotes]: In the paper "Cohen-Macauley and Gorenstein artin algebras", Auslander and Reiten have a short section about Auslander-Reiten theory in Gorenstein algebras (I always assume we have an artin algebra here). For Gorenstein algebras $A$ with Gorenstein dimension $g$, the category of Gorenstein projective modules has almost split sequences and the Auslander-Reiten translate of an object $C$ is given by the nonprojective part of the module $\Omega^gD\Omega^g Tr(C)$. Here are my questions:

Are there examples (of larger classes of Gorenstein algebras) in the literatur, where Auslander-Reiten quivers of the category of Gorenstein projectives has been calculated?
If there are only finitely many Gorenstein projective modules, one can build the direct sum $M$ of all such modules and calculate the endomorphism ring $B=End_A(M)$. Is there a relation between the Auslander-Reiten quiver of the Gorenstein projectives and the quiver of $B$ as is the case for "normal" Auslander algebras?
Are there useful tools to calculate the middle term in such an almost split sequence?

REPLY [4 votes]: Concerning Q3: In QPA one can compute (although I have not tested it extensively) almost split sequences in $^\perp T = \{ X\mid\operatorname{Ext}^i_\Lambda(X,T) = 0 \textrm{ for } i >0\}$ for a cotilting module $T$.  When $\Lambda$ is an admissible quotient of a path algebra and $\Lambda$ is Gorenstein, then letting $T = \Lambda$ gives you a way of computing in the category of Cohen-Macaulay modules. 
I hope that this is helpful.
Best regards, the QPA-team.
Command:
AlmostSplitSequenceInPerpT( T, M );

where $T$ is the cotilting module and $M$ is an indecomposable module in $^\perp T\setminus \operatorname{add T}$.