论文标题
无限多个变量中多项式环上的Spe平机模块
Sp-equivariant modules over polynomial rings in infinitely many variables
论文作者
论文摘要
我们研究了无限可变多项式环上的SP均衡模块的类别，其中SP表示无限的互合式组。我们建立了有关此类别的许多结果：例如，我们表明每个有限生成的模块M均拟合到一个精确的三角形$ t \到m \ to f \ to $ to $的情况下，其中t是扭转模块的有限长度复合物，F是“ free”模块的有限长度复合物；我们确定Grothendieck组；我们（部分）确定了注射模块的结构。我们应用这些结果表明，扭曲的交换代数$ {\ rm sym}（{\ bf c}^{\ iftty} \ oplus \ oplus \ bigWedge^2 {\ bf c}^{\ bf c}^{\ infty}）$ {\ rm sym}^2 {\ bf c}^{\ infty}）$是noetherian，这是迄今为止最强的结果。我们还表明，免费的2步nilpotent扭曲的谎言代数和谎言superalgebra是Noetherian的。
We study the category of Sp-equivariant modules over the infinite variable polynomial ring, where Sp denotes the infinite symplectic group. We establish a number of results about this category: for instance, we show that every finitely generated module M fits into an exact triangle $T \to M \to F \to$ where T is a finite length complex of torsion modules and F is a finite length complex of "free" modules; we determine the Grothendieck group; and we (partially) determine the structure of injective modules. We apply these results to show that the twisted commutative algebras ${\rm Sym}({\bf C}^{\infty} \oplus \bigwedge^2{\bf C}^{\infty})$ and ${\rm Sym}({\bf C}^{\infty} \oplus {\rm Sym}^2{\bf C}^{\infty})$ are noetherian, which are the strongest results to date of this kind. We also show that the free 2-step nilpotent twisted Lie algebra and Lie superalgebra are noetherian.
