Superpotentials and higher order derivations
Superpotentials and higher order derivations
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DOI：
10.1016/j.jpaa.2009.07.013
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发表时间：
2008-02
影响因子：
0.8
通讯作者：
Raf Bocklandt;T. Schedler;M. Wemyss
中科院分区：
文献类型：
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作者：
Raf Bocklandt;T. Schedler;M. Wemyss
我们认为代数定义的箭图的关系是k阶导数的超势，推广结果的Dubois，Violette的情况下。我们给出了一个建设兼容的森田等价，并表明，许多重要的代数出现在这种方式，包括McKay对应代数GLn为所有n，和四维Sklyanin代数。更一般地，我们证明了任何N-Koszul，（扭曲）Calabi-Yau代数必须有（扭曲）超势，并构造其最小分辨率的（扭曲）超势的导数。这给出了N-Koszul扭Calabi-Yau代数A和由超势ω定义的代数之间的等价性，使得相关复形是A的双模分解。最后，我们应用这些结果给出了四维Sklyanin代数的模空间的一个描述，使用SL 2（Z/4）的扩张的Weil表示。
We consider algebras defined from quivers with relations that are kth order derivations of a superpotential, generalizing results of Dubois-Violette to the quiver case. We give a construction compatible with Morita equivalence, and show that many important algebras arise in this way, including McKay correspondence algebras for GLnfor all n, and four-dimensional Sklyanin algebras. More generally, we show that any N-Koszul, (twisted) Calabi–Yau algebra must have a (twisted) superpotential, and construct its minimal resolution in terms of derivations of the (twisted) superpotential. This yields an equivalence between N-Koszul twisted Calabi–Yau algebras A and algebras defined by a superpotential ω such that an associated complex is a bimodule resolution of A. Finally, we apply these results to give a description of the moduli space of four-dimensional Sklyanin algebras using the Weil representation of an extension of SL2(Z/4).