操作数 II 上的不稳定数组

IF 0.8 4区数学 Q2 MATHEMATICS

Homology Homotopy and Applications Pub Date : 2024-02-21 DOI:10.4310/hha.2024.v26.n1.a4

Sacha Ikonicoff

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引用次数: 0

摘要

我们在有限域 $\mathbb{F}_q$ 上工作。我们引入了在操作数 $\P$ 上的不稳定 $P$-gebra 的概念。我们证明由不稳定模块自由生成的不稳定 $\P$- 代数在合适的条件下本身就是一个自由 $\P$- 代数。我们引入了一个"$q$级 "操作数族，它允许我们用自由的不稳定的$q$级代数来识别布朗-吉特勒、米勒和卡尔松所研究的不稳定模块。

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Unstable algebras over an operad II

$\def\P\{\mathcal{P}}$We work over the finite field $\mathbb{F}_q$. We introduce a notion of unstable $\P$-algebra over an operad $\P$. We show that the unstable $\P$-algebra freely generated by an unstable module is itself a free $\P$-algebra under suitable conditions. We introduce a family of ‘$q$-level’ operads which allows us to identify unstable modules studied by Brown–Gitler, Miller and Carlsson in terms of free unstable $q$-level algebras.

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来源期刊

Homology Homotopy and Applications 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Homology, Homotopy and Applications is a refereed journal which publishes high-quality papers in the general area of homotopy theory and algebraic topology, as well as applications of the ideas and results in this area. This means applications in the broadest possible sense, i.e. applications to other parts of mathematics such as number theory and algebraic geometry, as well as to areas outside of mathematics, such as computer science, physics, and statistics. Homotopy theory is also intended to be interpreted broadly, including algebraic K-theory, model categories, homotopy theory of varieties, etc. We particularly encourage innovative papers which point the way toward new applications of the subject.