Coverings and truncations of graded self-injective algebras

Let Λ be a graded self-injective algebra. We describe its smash product with the group Z, its Beilinson algebra and their relationship. Starting with Λ, we construct algebras with finite global dimension, called τ-slice algebras, we show that their trivial extensions are all isomorphic, and their repetitive algebras are the same as . There exist τ-mutations similar to the BGP reflections for the τ-slice algebras.