论文标题
Quaternionic投影转换的分类和分解
Classification and Decomposition of Quaternionic Projective Transformations
论文作者
论文摘要
我们考虑投影线性组$ \ mathrm {psl}（3，\ mathbb {h}）$。我们已经研究了该组中的可逆性问题，并使用可逆性提供了$ \ mathrm {psl}的动态类型的代数表征（3，3，\ mathbb {h}）$。我们进一步将$ \ mathrm {sl}（3，\ mathbb {h}）$的元素分解为简单元素的产品，其中元素$ g $ in $ \ mathrm {sl}（3，\ mathbb {h} $ \ mathrm {sl}（3，\ mathbb {r}）$。我们还重新审视了真正的投射转换，并遵循高盛的想法，为$ \ mathrm {sl}的元素提供了完整的分类（3，\ mathbb {r}）$。
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 $\mathrm{SL }(3,\mathbb{R})$.
