On Derived Equivalences for Selfinjective Algebras
On Derived Equivalences for Selfinjective Algebras
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DOI：
10.1080/00927870600938472
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发表时间：
2006-12
影响因子：
0.7
通讯作者：
Hiroki Abe;M. Hoshino
中科院分区：
文献类型：
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作者：
Hiroki Abe;M. Hoshino
证明了：若A是表示有限自内射Artin代数，则每个P · ∈ K B（𝒫A）满足Hom K（Mod−A）（P ·，P ·[i]）= 0，且add（P ·）= add（νP ·）是一个倾斜复形的直和项，若A，B是导出的等价表示有限自内射Artin代数，则存在一个自内射Artin代数序列A = B 0，B 1，.，B m = B使得对任意0 ≤ i < m，B +1是长度≤ 1的倾斜复形的自同态代数。
We show that if A is a representation-finite selfinjective Artin algebra, then every P • ∈ K b(𝒫 A ) with Hom K(Mod−A)(P •,P •[i]) = 0 for i ≠ 0 and add(P •) = add(νP •) is a direct summand of a tilting complex, and that if A, B are derived equivalent representation-finite selfinjective Artin algebras, then there exists a sequence of selfinjective Artin algebras A = B 0, B 1,…, B m = B such that, for any 0 ≤ i < m, B i+1 is the endomorphism algebra of a tilting complex for B i of length ≤ 1.