Commutativity of localized self-homotopy groups of symplectic groups

Daisuke Kishimoto; Akira Kono; Tomoaki Nagao

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Commutativity of localized self-homotopy groups of symplectic groups

机译：辛群的局部同伦群的可交换性

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摘要

The self-homotopy group of a topological group C is the set of homotopy classes of self-maps of G equipped with the group structure inherited from C. We determine the set of primes p such that the p-localization of the self-homotopy group of Sp(n) is commutative. As a consequence, we see that this group detects the homotopy commutativity of p-localized Sp(n) by its commutativity almost all cases.

机译：拓扑组C的自同构群是G的自映射的同伦类的集合，这些自映射具有从C继承的群结构。我们确定素数p的集合，以使自同构群的p局域化Sp（n）的可交换性。结果，我们看到该组几乎在所有情况下都通过其可交换性检测到了p局部Sp（n）的同伦可交换性。

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来源
《Topology and its applications》 |2011年第8期|p.1025-1032|共8页
作者
Daisuke Kishimoto; Akira Kono; Tomoaki Nagao;
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作者单位

Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan;

Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan;

Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan;

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原文格式 PDF
正文语种 eng
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关键词
self-homotopy group; symplectic group; commutativity;

机译：自同性群;折衷群;可交换性;

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1. Commutativity of the group of self-homotopy classes of Lie groups [J] . Kono A., Oshima H. Bulletin of the London Mathematical Society . 2004,第1期

机译：Lie群的自同伦类群的可交换性
2. The gap between near commutativity and almost commutativity in symplectic category [J] . Lev Buhovski Electronic Research Announcements in Mathematical Sciences . 2013,第12期

机译：辛范畴中近可交换性与几乎可交换性之间的差距
3. On Localized Unstable K~1-groups and Applications to Self-homotopy Groups [J] . Daisuke Kishimoto, Akira Kono, Mitsunobu Tsutaya Canadian Mathematical Bulletin . 2014,第2期

机译：局部不稳定的K〜1-基团及其在自同构群中的应用
4. Formation of the New Multi-sender Authentication Codes Via Symplectic Space through Finite Commutative Rings with Applications [C] . Wachirapong Jirakitpuwapat, Poom Kumam, Parin Chaipunya, International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology . 2021

机译：通过带有应用程序的有限换向环通过辛的空间形成新的多发送者认证代码
5. Quivers, representation theory, non-commutative symplectic geometry, stratifications and singular symplectic quotients. [D] . Diatta, Bassirou. 2004

机译：颤抖，表示论，非交换辛几何，分层和奇辛商。
6. Thermodynamical Extension of a Symplectic Numerical Scheme with Half Space and Time Shifts Demonstrated on Rheological Waves in Solids [O] . Tamás Fülöp, Róbert Kovács, Mátyás Szücs, 2020

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7. Commutativity of localized self-homotopy groups of symplectic groups [O] . Kishimoto Daisuke, Kono Akira, Nagao Tomoaki 2011

机译：辛群的局部同伦群的可交换性

Commutativity of localized self-homotopy groups of symplectic groups

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