We show that much of the theory of finite tight frames can be generalised to vector spaces over the quaternions. This includes the variational characterisation, group frames, and the characterisations of projective and unitary equivalence. We are particularly interested in sets of equiangular lines (equi-isoclinic subspaces) and the groups associated with them, and how to move them between the spaces $\Rd$, $\Cd$ and $\Hd$. We discuss what the analogue of Zauner's conjecture for equiangular lines in $\Hd$ might be.

翻译：本文证明了有限紧框架理论的大部分内容可以推广到四元数向量空间。这包括变分特征刻画、群框架，以及投影等价与酉等价的特征刻画。我们特别关注等角线（等斜子空间）的集合及其相关群，并研究如何在空间 $\Rd$、$\Cd$ 和 $\Hd$ 之间迁移这些结构。我们探讨了关于 $\Hd$ 中等角线的 Zauner 猜想在四元数情形下的可能类比形式。