Graded self-injective algebras "are" trivial extensions
Graded self-injective algebras "are" trivial extensions
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DOI：
10.1016/j.jalgebra.2009.05.034
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发表时间：
2009-03
期刊：
影响因子：
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通讯作者：
Xiao-Wu Chen
中科院分区：
文献类型：
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作者：
Xiao-Wu Chen
对正阶化Artin代数A= A_n_n ~ 0，引入了它的Beilinson代数B（A）.证明了若A是良分次自内射，则分次A-模范畴等价于平凡扩张代数T（B（A））上的分次模范畴.因此，存在从B（A）的有界导范畴到A上分次模的稳定范畴的全正合嵌入;它是等价的当且仅当第0分支代数A0具有有限的整体维数。
For a positively graded artin algebra A=⊕n⩾0Anwe introduce its Beilinson algebra b(A). We prove that if A is well-graded self-injective, then the category of graded A-modules is equivalent to the category of graded modules over the trivial extension algebra T(b(A)). Consequently, there is a full exact embedding from the bounded derived category of b(A) into the stable category of graded modules over A; it is an equivalence if and only if the 0-th component algebra A0has finite global dimension.