Structures of AS-regular Algebras
Structures of AS-regular Algebras
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发表时间：
2010
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通讯作者：
H. Minamoto;I. Mori
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作者：
H. Minamoto;I. Mori
本文对N-分次代数定义了AS-Gorenstein代数的概念，证明了Gorenstein参数为1的对称AS-正则代数是拟Fano代数的恰预投射代数.这个结果可以与Gorenstein参数为−1的对称分次Frobenius代数恰好是有限维代数的平凡扩张的事实相比较。本文的结果表明，非交换代数几何中的分类问题与有限维代数表示论中的分类问题之间存在着很强的相互作用。
In this paper, we define a notion of AS-Gorenstein algebra for N-graded algebras, and show that symmetric AS-regular algebras of Gorenstein parameter 1 are exactly preprojective algebras of quasi-Fano algebras. This result can be compared with the fact that symmetric graded Frobenius algebras of Gorenstein parameter −1 are exactly trivial extensions of finite dimensional algebras. The results of this paper suggest that there is a strong interaction between classification problems in noncommutative algebraic geometry and those in representation theory of finite dimensional algebras.