تقرير
Crossed modules
| العنوان: | Crossed modules |
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| المؤلفون: | Huebschmann, Johannes |
| المصدر: | Notices Amer. Math. Soc. 70 (2023), 1802-1813 |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Group Theory, Mathematics - Algebraic Topology, 01A60 12G05 18G45 20J05 57M10 |
| الوصف: | This is an overview of the idea of a crossed module. For a group, the triple that consists of the group, its group of automorphisms, and the canonical homomorphism from the group to its group of automorphisms constitutes a crossed module. Crossed modules arise from the identities among the relations of the presentation of a group, from the extension problem for groups and, more generally, in low dimensional topology. Also, the (successful) attempt to extend the idea of a normal extension of commutative fields to the realm of non-commutative algebras leads to crossed modules. Crossed modules appear implicitly in a forgotten paper by A. Turing which in principle settles the extension problem for groups. Crossed modules make perfect sense for Lie algebras. Comment: 17 pages |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1090/noti2831 |
| URL الوصول: | http://arxiv.org/abs/2403.15900 |
| رقم الأكسشن: | edsarx.2403.15900 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1090/noti2831 |
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