Product of two involutions in quaternionic special linear group
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913811380830208 |
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| author | Gongopadhyay, Krishnendu Lohan, Tejbir Maity, Chandan |
| author_facet | Gongopadhyay, Krishnendu Lohan, Tejbir Maity, Chandan |
| contents | An element of a group is called reversible if it is conjugate to its own inverse. Reversible elements are closely related to strongly reversible elements, which can be expressed as a product of two involutions. In this paper, we classify the reversible and strongly reversible elements in the quaternionic special linear group $\mathrm{SL}(n,\mathbb{H})$ and quaternionic projective linear group $ \mathrm{PSL}(n,\mathbb{H})$. We prove that an element of $ \mathrm{SL}(n,\mathbb{H})$ (resp. $ \mathrm{PSL}(n,\mathbb{H})$) is reversible if and only if it is a product of two skew-involutions (resp. involutions). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01587 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Product of two involutions in quaternionic special linear group Gongopadhyay, Krishnendu Lohan, Tejbir Maity, Chandan Group Theory Geometric Topology 20E45, 15B33 (Primary) 15A21, 20H25 (Secondary) An element of a group is called reversible if it is conjugate to its own inverse. Reversible elements are closely related to strongly reversible elements, which can be expressed as a product of two involutions. In this paper, we classify the reversible and strongly reversible elements in the quaternionic special linear group $\mathrm{SL}(n,\mathbb{H})$ and quaternionic projective linear group $ \mathrm{PSL}(n,\mathbb{H})$. We prove that an element of $ \mathrm{SL}(n,\mathbb{H})$ (resp. $ \mathrm{PSL}(n,\mathbb{H})$) is reversible if and only if it is a product of two skew-involutions (resp. involutions). |
| title | Product of two involutions in quaternionic special linear group |
| topic | Group Theory Geometric Topology 20E45, 15B33 (Primary) 15A21, 20H25 (Secondary) |
| url | https://arxiv.org/abs/2410.01587 |