Gentle \(m\)-Calabi-Yau tilted algebras

Abstract

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