Examples of tilting-discrete self-injective algebras which are not silting-discrete

In this paper, we introduce the notion of \nu-stable silting-discrete algebras, which unify silting-discrete algebras and tilting-discrete self-injective algebras, where \nu is a triangle auto-equivalence of the bounded homotopy category of finitely generated projective modules. Moreover, we give an example of tilting-discrete self-injective algebras which are not silting-discrete.