Coverings and Truncations of Graded Selfinjective Algebras

Abstract

Let $\Lambda$ be a graded self-injective algebra. We describe its smash product $Λ# k\mathbb Z^*$ with the group $\mathbb{Z}$, 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 $Λ# k\mathbb Z^*$. There exist $\tau$-mutations similar to the BGP reflections for the $\tau$-slice algebras. We also recover Iyama's absolute $n$-complete algebra as truncation of the Koszul dual of certain self-injective algebra.

arXiv commentManuscript revised, introduction and abstract rewritten