Finite quaternionic matrix groups
Represent. Theory 2 (1998), 106-223.

Gabriele Nebe
Lehrstuhl B f\"ur Mathematik, RWTH Aachen, Templergraben 64, 
52062 Aachen, Germany

Abstract. Let $\mathcal D$ be a definite quaternion algebra such that its 
center has degree $d$ over $\mathbb Q$. A subgroup $G$ of $GL_n(\mathcal D)$ 
is absolutely irreducible if the $\mathbb Q$-algebra spanned by the matrices 
in $G$ is $\mathcal D^{n \times n}$. The finite absolutely irreducible 
subgroups of $GL_n(\mathcal D)$ are classified for $nd \le 10$ by constructing
representatives of the conjugacy classes of the maximal finite ones. Methods 
to construct the groups and to deal with the quaternion algebras are developed.
The investigation of the invariant rational lattices yields quaternionic 
structures for many interesting lattices.