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Sep 1, 2017 at 16:41 comment added Mare @JeremyRickard thanks, yes A is not Gorenstein and the other is selfinjective. Thanks for the great answer. Looked like hard work.
Sep 1, 2017 at 16:35 comment added Jeremy Rickard By the way, does GAP confirm that $A$ is not Gorenstein but $B$ is?
Sep 1, 2017 at 16:32 comment added Jeremy Rickard I've checked by hand that those are isomorphic. If you eliminate the relations that say that the arrows all have square zero and commute with one another, you're left in both cases with relators in four generators $p,q,r,s$ of the form $pq,qr,rs, ps, pr-qs$, and for $A$ there are three other degree three relators that are redundant.
Sep 1, 2017 at 11:19 history answered Mare CC BY-SA 3.0