N-cluster tilting subcategories for radical square zero algebras

Abstract

We give a characterization of radical square zero bound quiver algebras k Q / J 2 that admit n -cluster tilting subcategories and n Z -cluster tilting subcategories in terms of Q . We also show that if Q is not of cyclically oriented extended Dynkin type A ˜ , then the poset of n -cluster tilting subcategories of k Q / J 2 with relation given by inclusion forms a lattice isomorphic to the opposite of the lattice of divisors of an integer which depends on Q .