Coverings and Truncations of Graded Selfinjective Algebras

Details Coverings and Truncations of Graded Selfinjective Algebras Coverings and Truncations of Graded Selfinjective Algebras

2010-02-26

arxiv.org/abs/1002.4910v3

Mathematics

Rings and Algebras

Manuscript revised, introduction and abstract rewritten

Scientific paper

Let $\Lambda$ be a graded self-injective algebra. We describe its smash product $\Lambda# k\mathbb Z^*$ 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 $\Lambda# k\mathbb Z^*$. 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.

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