Auslander-Reiten theory for Gorenstein algebras

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 $^\perp T\setminus \operatorname{add T}$.