Given a finite dimensional algebra $A$ over a field $K$ with $\Omega^i(D(A)) \cong \Omega^{i+1}(D(A))$ for some $i \geq 1$, where $D(A)=Hom_K(A,K)$.
Do we then also have $\Omega^{-i}(A) \cong \Omega^{-(i+1)}(A)$?
Question on syzygies
Mare
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