Some invariants of U(1,1;ℍ) and diagonalization

2023/06/21 by Cailing Yao, Yao, Cailing, Bingzhe Hou +3
Computer Science · Mathematics · #15A18 #15A20 #15B33 #16R30 (Secondary) #30G35 (Primary) #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Group Theory (math.GR) #Mathematics and Applications #Matrix Theory and Algorithms #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2306.12052

openalex publication_date 2023/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Denote by ℍ the set of all quaternions. We are interested in the group U(1,1;ℍ), which is a subgroup of 2× 2 quaternionic matrix group and is sometimes called Sp(1,1). As well known, U(1,1;ℍ) corresponds to the quaternionic Möbius transformations on the unit ball in ℍ. In this article, some similar invariants on U(1,1;ℍ) are discussed. Our main result shows that each matrix T∈ U(1,1;ℍ), which corresponds to an elliptic quaternionic Möbius transformation g_T(z), could be U(1,1;ℍ)-similar to a diagonal matrix.

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