ループのアイソトピー
出典: フリー百科事典『ウィキペディア（Wikipedia）』 (2023/12/19 17:24 UTC 版)
数学の 抽象代数学分野に於いて、アイソトピー (または イソトピー 英: isotopy) とは、ループ の代数的概念を分類するために使われる同値関係である。
注釈
- ^ 未訳: based on his slightly earlier definition of isotopy for algebras, which was in turn inspired by work of Steenrod.
- ^ The set of all autotopies of a quasigroup form a group with the automorphism group as a subgroup.
- ^ 原文: In this case the underlying sets of the quasigroups must be the same but the multiplications may differ.
- ^ 原文: A loop L is a G-loop if it is isomorphic to all its loop isotopes.
- ^ 原文: Choosing a different origin or exchanging the line classes may result in nonisomorphic coordinate loops.
- ^ 原文: In other words, two loops are isotopic if and only if they are equivalent from geometric point of view.
- ^ 原文: The group of autotopism of the loop corresponds to the group direction preserving collineations of the 3-net.
- ^ 原文: The set of companion elements is the orbit of the stabilizer of the axis in the collineation group.
- ^ 原文: The property P is universal if and only if it is independent on the choice of the origin
訳注
- ^ Then it is the product of the principal isotopy from and and the isomorphism between and .
[続きの解説]
「ループのアイソトピー」の続きの解説一覧
- 1 ループのアイソトピーとは
- 2 ループのアイソトピーの概要
- 3 準群のアイソトピー
- 4 ループのアイソトピー
- 5 ループの疑似自己同型
- 6 関連項目
- ループのアイソトピーのページへのリンク
