GRADED MORITA EQUIVALENCES FOR GEOMETRIC AS-REGULAR ALGEBRAS
GRADED MORITA EQUIVALENCES FOR GEOMETRIC AS-REGULAR ALGEBRAS
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DOI：
10.1017/s001708951200047x
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发表时间：
2012-08
影响因子：
0.5
通讯作者：
I. Mori;Kenta Ueyama
中科院分区：
文献类型：
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作者：
I. Mori;Kenta Ueyama
AS-正则代数的分类是非交换代数几何的重要课题之一。本文研究了给定的AS-正则代数何时是分次Morita等价的。特别地，对每一个几何AS-正则代数A，我们定义了另一个分次代数A，并证明了如果两个几何AS-正则代数A和A'是分次Morita等价的，则A和A'同构为分次代数.我们还表明，在许多三维的情况下，匡威的。作为应用，我们将所得结果应用于Frobenius Koszul代数和Beilinson代数.
Abstract Classification of AS-regular algebras is one of the major projects in non-commutative algebraic geometry. In this paper, we will study when given AS-regular algebras are graded Morita equivalent. In particular, for every geometric AS-regular algebra A, we define another graded algebra A, and show that if two geometric AS-regular algebras A and A' are graded Morita equivalent, then A and A' are isomorphic as graded algebras. We also show that the converse holds in many three-dimensional cases. As applications, we apply our results to Frobenius Koszul algebras and Beilinson algebras.