Geodesic
Product of two involutions in quaternionic special linear group
Canadian mathematical bulletin, Tome 68 (2025) no. 2, pp. 421-439

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DOI

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).
DOI : 10.4153/S0008439524000699
Mots-clés : Reversible elements, strongly reversible elements, quaternionic special linear group, Weyr canonical form, reversing symmetry group 
Gongopadhyay, Krishnendu; Lohan, Tejbir; Maity, Chandan. Product of two involutions in quaternionic special linear group. Canadian mathematical bulletin, Tome 68 (2025) no. 2, pp. 421-439. doi: 10.4153/S0008439524000699
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     title = {Product of two involutions in quaternionic special linear group},
     journal = {Canadian mathematical bulletin},
     pages = {421--439},
     year = {2025},
     volume = {68},
     number = {2},
     doi = {10.4153/S0008439524000699},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439524000699/}
}
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