Generalized Split Quaternions and Their Applications on Non-Parabolic Conical Rotations

Abstract

In this study, we first generalize the Lorentzian inner and vector products, and then we define the generalized split quaternions by means of the generalized Lorentzian inner and vector products. Next, on any hyperboloid of one or two sheets, which is a generalized Lorentzian sphere, non-parabolic conical rotations with nonnull axes are expressed using the generalized split quaternions with supporting numerical examples.

Keywords

• Lorentzian inner product
• Lorentzian vector product
• Lorentzian rotation matrix
• Lorentzian symmetry
• split quaternion