1 results
Product of two involutions in quaternionic special linear group
- Part of
-
- Journal:
- Canadian Mathematical Bulletin , First View
- Published online by Cambridge University Press:
- 08 January 2025, pp. 1-19
-
- Article
- Export citation
-
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).
