Classification and Decomposition of Quaternionic Projective Transformations

Abstract

We consider the projective linear group $\mathrm{PSL}(3,\mathbb{H})$. We have investigated the reversibility problem in this group and use the reversibility to offer an algebraic characterization of the dynamical types of $\mathrm{PSL}(3,\mathbb{H})$. We further decompose elements of $\mathrm{SL}(3,\mathbb{H})$ as products of simple elements, where an element $g$ in $\mathrm{SL}(3,\mathbb{H})$ is called $\text{simple}$ if it is conjugate to an element of $\mathrm{SL}(3,\mathbb{R})$. We have also revisited real projective transformations and following Goldman's ideas, have offered a complete classification for elements of $\mathrm{SL}(3,\mathbb{R})$.

Final version, 20 pages

References in corpus (2)

• Reversibility of Hermitian Isometries
• Limit sets of cyclic quaternionic Kleinian groups

Cited by in corpus (1)

• Product of two involutions in quaternionic special linear group