We show that a finite dimensional monomial algebra satisfies the finite generation conditions of Snashall-Solberg for Hochschild cohomology if and only if it is Gorenstein. This gives, in the case of monomial algebras, the converse to a theorem of Erdmann-Holloway-Snashall-Solberg-Taillefer. We also give a necessary and sufficient combinatorial criterion for finite generation.
We classify the Betti tables of indecomposable graded matrix factorizations over the simple elliptic singularity f λ = XY (X − Y )(X − λY ) by making use of an associated weighted projective line of genus one.
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