Noncommutative deformations of modules
Noncommutative deformations of modules
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模的非交换变形
DOI：
10.4310/hha.2002.v4.n2.a17
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
O. A. Laudal
中科院分区：
文献类型：
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作者：
O. A. Laudal
推广了k-代数上模的经典变形理论，其中k是一个有限域。对任意k-代数和任意r-模的代数族，考虑定义在Artin r-点（不一定是交换的）k-代数范畴上的变形函子，证明了它有一个预表示的船体，它可以用Ext-群上的Massey型积计算.这是第一次用来构造具有一个简单的模的预分配集合的k-代数，并研究模的迭代扩张的模空间。在即将发表的论文中，我们将证明这种非交换变形理论是研究k-代数和建立非交换代数几何的有用工具。敬简-埃里克鲁什六十大寿
The classical deformation theory for modules on a k-algebra, where k is a Þeld, is generalized. For any k-algebra, and for any Þnite family of r modules, we consider a deformation functor deÞned on the category of Artinian r-pointed (not necessarily commutative) k-algebras, and prove that it has a prorepresenting hull, which can be computed using Massey-type products in the Ext-groups. This is Þrst used to construct k-algebras with a preassigned set of simple modules, and to study the moduli space of iterated extensions of modules. In forthcoming papers we shall show that this noncommutative deformation theory is a useful tool in the study of k-algebras, and in establishing a noncommutative algebraic geometry. To Jan–Erik Roos on his sixty–Þfth birthday