Product of two involutions in quaternionic special linear group

Abstract

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).

15 pages, To appear in Canadian Mathematical Bulletin. arXiv admin note: text overlap with arXiv:2307.07967

References in corpus (3)

• A factorization result for classical and similitude groups
• Reality of Unipotent elements in Classical Lie Groups
• Classification and Decomposition of Quaternionic Projective Transformations