Continuous Inverse Ambiguous Functions on Lie Groups
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918158625931264 |
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| author | Schmitz, David Rahman, Sadman Kindness, Anthony |
| author_facet | Schmitz, David Rahman, Sadman Kindness, Anthony |
| contents | In a previous study, the first author defines an inverse ambiguous function on a group $G$ to be a bijective function $f : G \to G$ 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 classical Lie groups. In particular, we look at tori, elliptic curves over various fields, vector spaces, additive matrix groups, and multiplicative matrix groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09958 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Continuous Inverse Ambiguous Functions on Lie Groups Schmitz, David Rahman, Sadman Kindness, Anthony Group Theory Geometric Topology 39B52 (Primary), 22E20 (Secondary) In a previous study, the first author defines an inverse ambiguous function on a group $G$ to be a bijective function $f : G \to G$ 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 classical Lie groups. In particular, we look at tori, elliptic curves over various fields, vector spaces, additive matrix groups, and multiplicative matrix groups. |
| title | Continuous Inverse Ambiguous Functions on Lie Groups |
| topic | Group Theory Geometric Topology 39B52 (Primary), 22E20 (Secondary) |
| url | https://arxiv.org/abs/2510.09958 |