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 $\textit{ simple}$ 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 $\mathrm{ SL }(3,\mathbb{ R})$.
Categories: math.GR math.GT