Coverings and truncations of graded self-injective algebras

Let Lambda be a graded self-injective algebra. We describe its smash product Lambda # kZ* with the group Z, its Beilinson algebra and their relationship. Starting with Lambda, we construct algebras with finite global dimension, called tau-slice algebras, we show that their trivial extensions are all isomorphic, and their repetitive algebras are the same as Lambda # kZ*. There exist tau-mutations similar to the BGP reflections for the tau-slice algebras. (C) 2012 Elsevier Inc. All rights reserved.