关于 FI 模块的尾部

Pub Date : 2024-06-03 DOI:10.1016/j.jpaa.2024.107741

Peter Patzt, John D. Wiltshire-Gordon

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引用次数: 0

摘要

我们研究整数值 FI 模块的末端行为。我们的第一个结果用新定义的尾不变式描述了 FI 模块的高度。我们的主要结果为我们称之为 FJ 的新范畴提供了 FI-尾和有限支持模块之间的等价性。FJ 的对象是自然数，态是无穷级数，其和取自列括号的某些模块。

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On the tails of FI-modules

We study the end-behavior of integer-valued $FI$ -modules. Our first result describes the high degrees of an $FI$ -module in terms of newly defined tail invariants. Our main result provides an equivalence of categories between $FI$ -tails and finitely supported modules for a new category that we call $FJ$ . Objects of $FJ$ are natural numbers, and morphisms are infinite series with summands drawn from certain modules of Lie brackets.

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