Selfinjective Koszul algebras of finite complexity
Selfinjective Koszul algebras of finite complexity
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DOI：
10.1007/s10114-009-6703-0
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发表时间：
2009-11
期刊：
影响因子：
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通讯作者：
J. Guo;Aihua Li;Qiuxian Wu
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文献类型：
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作者：
J. Guo;Aihua Li;Qiuxian Wu
本文研究了有限复杂性的自射Koszul代数。证明了当复杂度为有限时，复杂度为非负整数；并且证明了复杂度小于或等于tot的模范畴是分解和余分解的。证明了对于每一个0≤L≤m，对于V的外代数，存在一族复参数BYG(L，m)模，它是Anm维向量空间V的1维子空间的Grassman模.利用复杂性，通过二维向量空间外代数上SL(2，C)的有限子群的斜群代数，给出了特征为0的代数闭域上具有零根立方体的驯服对称代数表示理论的一种新方法.
In this paper, we study selfinjective Koszul algebras of finite complexity. We prove that the complexity is a nonnegative integer when it is finite; and that the category of modules with complexity less or equal tot, is resolving and coresolving. We show that for each 0 ≤l≤mthere exist a family of modules of complexitylparameterized byG(l,m), the Grassmannian ofl-dimensional subspaces of anm-dimensional vector spaceV, for the exterior algebra ofV. Using complexity, we also give a new approach to the representation theory of a tame symmetric algebra with vanishing radical cube over an algebraically closed field of characteristic 0, via skew group algebra of a finite subgroup of SL(2,C) over the exterior algebra of a 2-dimensional vector space.