The stable Picard group of \(\mathcal {A}(n)\)

IF 0.5 4区数学 Q2 MATHEMATICS

Journal of Homotopy and Related Structures Pub Date : 2025-10-24 DOI:10.1007/s40062-025-00387-4

JianZhong Pan, RuJia Yan

引用次数: 0

Abstract

In this paper, we show that, for \(n\ge 2\), the stable Picard group of \(\mathcal {A}(n)\) is \(\mathbb {Z}\oplus \mathbb {Z}\), where \(\mathcal {A}(n)\) is the usual finite sub Hopf algebra of the Steenrod algebra \(\mathcal {A}\) at the prime 2. The proof relies on reductions from a Hopf algebra to certain sub Hopf algebras.

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稳定的皮卡德群 \(\mathcal {A}(n)\)

本文证明，对于\(n\ge 2\), \(\mathcal {A}(n)\)的稳定Picard群为\(\mathbb {Z}\oplus \mathbb {Z}\)，其中\(\mathcal {A}(n)\)是Steenrod代数\(\mathcal {A}\)在素数2处通常的有限子Hopf代数。这个证明依赖于从一个Hopf代数到若干子Hopf代数的约简。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Homotopy and Related Structures MATHEMATICS-

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.