分次自内射代数的覆盖与截断
Coverings and Truncations of Graded Selfinjective Algebras
摘要：
设$Λ$是分次自内射代数.我们描述了它的Smash积$Λ# k\mathbb Z^*$与群$\mathbb Z$、它的Beilinson代数以及它们之间的关系。从$Λ$出发，构造了具有有限整体维数的$τ$ -片代数，证明了它们的平凡扩张都是同构的，并且它们的重复代数是相同的$Λ# k\mathbb Z^*$ .对于$τ$ -片代数，存在类似于BGP反射的$τ$ -突变.我们还恢复Iyama的绝对$n$ -完全代数作为截断的Koszul对偶的某些自内射代数。
英文摘要：
Let $Λ$ 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 $Λ$, 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 $Λ# k\mathbb Z^*$. There exist $τ$-mutations similar to the BGP reflections for the $τ$-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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