Quaternion generalization of super-Poincaré group. (English) Zbl 1450.83006
Summary: Super-Poincaré algebra in \(D = 6\) space-time dimensions has been studied in terms of quaternionic representation of Lorentz group. Starting the connection of quaternion Lorentz group with \(\mathrm{SO}(1, 5)\) group, the \(\mathrm{SL}(2, \mathbb H)\) spinors for Dirac and Weyl representations of Poincaré group are described consistently to extend the Poincaré algebra to super-Poincaré algebra for \(D = 6\) space-time.
MSC:
| 83E50 | Supergravity |
| 83A05 | Special relativity |
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 22E15 | General properties and structure of real Lie groups |
| 11R52 | Quaternion and other division algebras: arithmetic, zeta functions |
| 83C60 | Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism |
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