McKay‐type correspondence for AS‐regular algebras
McKay‐type correspondence for AS‐regular algebras
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DOI：
10.1112/jlms/jdt005
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发表时间：
2013-08
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影响因子：
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通讯作者：
I. Mori
中科院分区：
文献类型：
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作者：
I. Mori
经典的McKay对应表明，当G≤SL（2, k）是自然作用于k[x， y]的有限子群时，Spec k[x， y]G的最小分辨率等价于G的McKay振子的预投影代数。在本文中，我们将看到，对于自然作用于n个变量的AS -正则代数的有限循环子群G≤GL（n, k）也存在类似的对应关系。由于AS正则代数是多项式代数的非交换类似物，这可以被认为是非交换代数几何中的McKay型对应。
The classical McKay correspondence claims that the minimal resolution of Spec k[x, y]G where G ⩽ SL(2, k) is a finite subgroup naturally acting on k[x, y] is derived equivalent to the preprojective algebra of the McKay quiver of G. In this paper, we will see that there is a similar correspondence in the case of a finite cyclic subgroup G ⩽ GL(n, k) naturally acting on an AS‐regular algebra in n variables. Since AS‐regular algebras are non‐commutative analogues of polynomial algebras, this can be thought of as a McKay‐type correspondence in non‐commutative algebraic geometry.