Quaternions for Guts

Abstract

We derive an appropriate definition of transpose for quaternionic matrices and give a new panoramic review of the quaternionic groups. We aim to analyse possible quaternionic groups for GUTs.

16 pages, Latex

References in corpus (6)

• Generalized quantum dynamics
• Quaternions and Special Relativity
• Composite leptons and quarks constructed as triply occupied quasiparticles in quaternionic quanutm mechanics
• Representations of U(1,q) and Constructive Quaternion Tensor Products
• Translations between Quaternion and Complex Quantum Mechanics
• Duffin-Kemmer-Petiau equation on the quaternion field

Cited by in corpus (13)

• Right eigenvalue equation in quaternionic quantum mechanics
• Octonionic Electrodynamics
• Quaternionic differential operators
• $SU(3{)}_C\times SU(2{)}_L\times U(1{)}_Y\left(\times U(1{)}_X\right)$ as a symmetry of division algebraic ladder operators
• Matrix Representation of Octonions and Generalizations
• Octonionic Representations of GL(8,R) and GL(4,C)
• Quaternions in mathematical physics (1): Alphabetical bibliography
• Rotations in the Space of Split Octonions
• Quaternionic Electroweak Theory and CKM Matrix
• Spontaneous Symmetry Breaking in Presence of Electric and Magnetic Charges
• The quaternionic determinat
• An Algebraic Roadmap of Particle Theories, Part I: General construction
• An Algebraic Roadmap of Particle Theories, Part II: Theoretical checkpoints