2015/05/31 by Tony Thrall, Thrall, Tony
Mathematics · Physics and Astronomy · #30-01 #Advanced Mathematical Theories and Applications #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Mathematics and Applications #math.CV #msc:30-01
paper · pdf · doi:10.48550/arxiv.1506.00274
arxiv created 2015/05/31 · openalex publication_date 2015/05/31 · arxiv updated 2015/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Möbius transformations of the extended complex plane are at the crossroads of many interesting topics, e.g., they form a group under composition, are the simplest form of rational function, and are a path to Lie theory. Quaternionic transformations are a subgroup of Möbius transformations isomorphic to rotations of the Riemann sphere, which also represent quaternion conjugation. These representations yield formulas for the axis and radians of rotation, and thereby portray each particular quaternionic transformation as part of a continuous orbit of rotations sharing a common axis.