TITLE:
Split-Tetraquaternion Algebra and Applications
AUTHORS:
Grégoire Lutanda Panga
KEYWORDS:
Tetraquaternion Algebra, Split-Tetraquaternion Algebra, Split Quaternion Algebra, Clifford Algebra
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.12 No.7,
July
31,
2024
ABSTRACT: In this paper, from the spacetime algebra associated with the Minkowski space
ℝ
3,1
by means of a change of signature, we describe a quaternionic representation of the split-tetraquaternion algebra which incorporates the Pauli algebra, the split-biquaternion algebra and the split-quaternion algebra, we relate these algebras to Clifford algebras and we show the emergence of the stabilized Poincaré-Heisenberg algebra from the split-tetraquaternion algebra. We list without going into details some of their applications in Physics and in Born geometry.