GL-EQUIVARIANT MODULES OVER POLYNOMIAL RINGS IN INFINITELY MANY VARIABLES. II
GL-EQUIVARIANT MODULES OVER POLYNOMIAL RINGS IN INFINITELY MANY VARIABLES. II
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DOI：
10.1090/tran/8496
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发表时间：
2012-06
期刊：
影响因子：
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通讯作者：
Steven V. Sam;A. Snowden
中科院分区：
文献类型：
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作者：
Steven V. Sam;A. Snowden
扭交换代数在表示稳定性的新兴领域中扮演着重要的角色。设$A_{d}$是由$d$个1次不定元自由生成的tca。在前一篇文章中，我们确定了$A_{1}$ -模范畴（它等价于$\mathbf{FI}$ -模范畴）的结构。在本文中，我们建立了$A_{d}$ -模范畴的类似结果，对任意的$d$ . $A_{d}$上的模与作者在以前研究塞格雷和Veronese嵌入合冲时所使用的结构密切相关，我们希望本文的结果最终能导致对这些工作的改进。我们的结果在渐近交换代数中也有意义。
Twisted commutative algebras (tca’s) have played an important role in the nascent field of representation stability. Let $A_{d}$ be the tca freely generated by $d$ indeterminates of degree 1. In a previous paper, we determined the structure of the category of $A_{1}$ -modules (which is equivalent to the category of $\mathbf{FI}$ -modules). In this paper, we establish analogous results for the category of $A_{d}$ -modules, for any $d$ . Modules over $A_{d}$ are closely related to the structures used by the authors in previous works studying syzygies of Segre and Veronese embeddings, and we hope the results of this paper will eventually lead to improvements on those works. Our results also have implications in asymptotic commutative algebra.