{"title":"李群上的连续逆二义函数","authors":"David Schmitz, Sadman Rahman, Anthony Kindness","doi":"10.1007/s00010-024-01131-8","DOIUrl":null,"url":null,"abstract":"<div><p>In Schmitz (Aequ Math 91:373–389, 2017), the first author defines an inverse ambiguous function on a group <i>G</i> to be a bijective function <span>\\(f: G \\rightarrow G\\)</span> satisfying the functional equation <span>\\(f^{-1}(x) = f(x^{-1})\\)</span> for all <span>\\(x \\in G\\)</span>. In this paper, we investigate the existence of continuous inverse ambiguous functions on various Lie groups. In particular, we look at tori, elliptic curves over various fields, vector spaces, additive matrix groups, and multiplicative matrix groups.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 3","pages":"1357 - 1369"},"PeriodicalIF":0.7000,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Continuous inverse ambiguous functions on Lie groups\",\"authors\":\"David Schmitz, Sadman Rahman, Anthony Kindness\",\"doi\":\"10.1007/s00010-024-01131-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In Schmitz (Aequ Math 91:373–389, 2017), the first author defines an inverse ambiguous function on a group <i>G</i> to be a bijective function <span>\\\\(f: G \\\\rightarrow G\\\\)</span> satisfying the functional equation <span>\\\\(f^{-1}(x) = f(x^{-1})\\\\)</span> for all <span>\\\\(x \\\\in G\\\\)</span>. In this paper, we investigate the existence of continuous inverse ambiguous functions on various Lie groups. In particular, we look at tori, elliptic curves over various fields, vector spaces, additive matrix groups, and multiplicative matrix groups.</p></div>\",\"PeriodicalId\":55611,\"journal\":{\"name\":\"Aequationes Mathematicae\",\"volume\":\"99 3\",\"pages\":\"1357 - 1369\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-10-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Aequationes Mathematicae\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00010-024-01131-8\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Aequationes Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00010-024-01131-8","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
在Schmitz (Aequ Math 91:373-389, 2017)中,第一作者定义了群G上的逆二义函数为双射函数\(f: G \rightarrow G\),满足所有\(x \in G\)的函数方程\(f^{-1}(x) = f(x^{-1})\)。本文研究了各种李群上连续二义逆函数的存在性。特别地,我们看环面,椭圆曲线在各种领域,向量空间,加性矩阵群,和乘法矩阵群。
Continuous inverse ambiguous functions on Lie groups
In Schmitz (Aequ Math 91:373–389, 2017), the first author defines an inverse ambiguous function on a group G to be a bijective function \(f: G \rightarrow G\) satisfying the functional equation \(f^{-1}(x) = f(x^{-1})\) for all \(x \in G\). In this paper, we investigate the existence of continuous inverse ambiguous functions on various Lie groups. In particular, we look at tori, elliptic curves over various fields, vector spaces, additive matrix groups, and multiplicative matrix groups.
期刊介绍:
aequationes mathematicae is an international journal of pure and applied mathematics, which emphasizes functional equations, dynamical systems, iteration theory, combinatorics, and geometry. The journal publishes research papers, reports of meetings, and bibliographies. High quality survey articles are an especially welcome feature. In addition, summaries of recent developments and research in the field are published rapidly.