Gentle $m$-Calabi-Yau tilted algebras

Abstract

We prove that all gentle 2-Calabi-Yau tilted algebras (over an algebraically closed field) are Jacobian, moreover their bound quiver can be obtained via block decomposition. Related families of gentle $(m+1)$-Calabi-Yau tilted algebras are the $m$-cluster-tilted algebras of type $\mathbb{A}$ and $\tilde{\mathbb{A}}$. For these algebras we prove that a module $M$ is stable Cohen-Macaulay if and only if ${\Omega }^{m+1}\tau M\simeq M$.

12 pages - 10 figures (v3: example corrected, char 3 case considered, minor edition)

References in corpus (3)

• 2-CY-tilted algebras that are not Jacobian
• M-cluster tilted algebras of type A tilde
• Finite-dimensional algebras are (m>2)-Calabi-Yau-tilted

Cited by in corpus (3)

• A geometric model for the derived category of gentle algebras
• On extensions for gentle algebras
• Higher gentle algebras