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Mar 19 at 0:39 comment added Aaron Bergman Isn’t this Butler and King? sciencedirect.com/science/article/pii/S0021869398975998
Mar 18 at 18:51 comment added It'sMe If you have a particular representation in mind then you can calculate the projective resolution using the QPA package in GAP. They have command for calculating projective resolution. You can find more information about it here: gap-system.org/Packages/qpa.html
Mar 18 at 17:41 comment added Hugh Thomas This boils down to (repeatedly) finding a (minimal) projective cover, which just means finding a minimal generating set.
Mar 18 at 11:45 comment added user52991 Yes, I want to understand how exactly to construct the resolution.
Mar 18 at 9:22 comment added Dave Benson In general, if there are no directed cycles, then the global dimension is finite. It is bounded by the length of the longest directed path.
Mar 18 at 6:21 history asked user52991 CC BY-SA 4.0