Singularity categories of some 2-CY-tilted algebras

Ming Lu

Published 2015-09-18Version 1

We define a class of 2-CY-tilted algebras, which are called (simple) polygon-tree algebras, as a generalization of cluster-tilted algebras of type D. Using a suitable process of mutations of quivers with potentials (which are also BB-mutations) inducing derived equivalences, and one-pointed (co)extensions which preserve singularity equivalences, we find a connected selfinjective Nakayama algebra singularity equivalent to each simple polygon-tree algebra. Furthermore, we also give a classification of this kind of algebras up to representation type.