G-algebras, Twistings, and Equivalences of Graded Categories
G-algebras, Twistings, and Equivalences of Graded Categories
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G 代数、扭曲和分级范畴的等价
DOI：
10.1007/s10468-009-9193-y
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发表时间：
2006
影响因子：
0.6
通讯作者：
S. Sierra
中科院分区：
文献类型：
--
作者：
S. Sierra
给定${\mathbb Z}$-分次环A和B，我们问分次模范畴GR-A和GR-B何时等价。利用$M athbb Z}$-代数，我们将Arhn-Márki和Del Río的Morita-型结果与张引入的扭系联系起来，并证明了：例如：定理如果A和B是$\mathbb Z}$-分次环，则：(1)A同构于B的张扭转当且仅当$-代数$\overline{A}=\bigoplus_{i，j\in{mathbb Z}}A_{j-i}$和$\overline{B}=\bigoplus_{i，J\in{\mathbb Z}}B_{j-i}$同构。(2)如果A和B与A1 ≠ 0分次连通，则GR-A ≃ GR- B当且仅当$\OVERLINE{A}$和$\OVERLINE{B}$同构。这简化和推广了张的结果。
Given ${\mathbb Z}$-graded rings A and B, we ask when the graded module categories gr-A and gr-B are equivalent. Using ${\mathbb Z}$-algebras, we relate the Morita-type results of Áhn-Márki and del Río to the twisting systems introduced by Zhang, and prove, for example: TheoremIf A and B are ${\mathbb Z}$-graded rings, then: (1) A is isomorphic to a Zhang twist of B if and only if the ${\mathbb Z}$-algebras $\overline{A} = \bigoplus_{i,j \in {\mathbb Z}} A_{j-i}$ and $\overline{B} = \bigoplus_{i,j \in {\mathbb Z}} B_{j-i}$ are isomorphic. (2) If A and B are connected graded with A1 ≠ 0, then gr-A ≃ gr- B if and only if $\overline{A}$ and $ \overline{B}$ are isomorphic. This simplifies and extends Zhang’s results.