1. This site uses cookies. By continuing to use this site, you are agreeing to our use of cookies. Learn More.

Question on syzygies

Discussion in 'Mathematics' started by Mare, Oct 8, 2018.

  1. Mare

    Mare Guest

    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 $\Omega^{-i}(A) \cong \Omega^{-(i+1)}(A)$?

    In case the answer is yes, do we even have that $\Omega^{-i}(A)$ and $\Omega^i(D(A))$ have the same vector space dimension? (Note that a positive answer would prove the Gorenstein symmetry conjecture)

    Login To add answer/comment
     

Share This Page