Quaternlonic möbius transformations and loxodromes

Abstract

One-parameter families of quaternionic linear-fractional transformations are defined in terms of the exponential mapping from the Lie algebra of PSL₂ H. The invariance of loxodromic curves allows us to characterize the fixed points corresponding to the family exp(tX) in terms of the generator X∈ sl₂ H. Certain degenerate cases are described; it is shown that for nonplanar loxodromes the generator is unique.

Keywords:

• Quaternion
• Möbius transformation
• loxodrome
• lie algebra

Classification Categories::

• 51B10
• 20G20
• 15A66

^*Partially supported by CONACyT grant 211085-5-2585P-E.

^*Partially supported by CONACyT grant 211085-5-2585P-E.

Notes

^*Partially supported by CONACyT grant 211085-5-2585P-E.