Geometry of skew-Hermitian matrices
The paper is organized as follows. In Section 2, automorphisms of division rings of generalized quaternions are studied. In Section 3, parallel to the geometry of Hermitian matrices maximal sets of rank 1 and rank 2 in the geometry of skew-Hermitian matrices are introduced and studied. In Section 4, when \(n= 2\), the affine space structure of any maximal set of rank 2 is introduced. In Section 5, Theorem 1.1 for the case \(n= 2\) is proved. Section 6 concludes the proof of Theorem 1.1. At the end of Section 6, it is pointed out that the condition \({\mathcal A}^{-1}\) preserving the adjacency in Theorem 1.1 can be omitted.
Division ring of generalized quaternions
scientific article; zbMATH DE number 2136675