Abstract
The Cayley–Klein parameters for the de Sitter groups SO(4, 1) and SO(3, 2) are introduced, and in an extension of the earlier investigation of quasigroups connected with Clifford groups, quasigroups connected with the SO(4, 1) and SO(3, 2) groups are determined. It is shown that these quasigroups have eight-dimensional, double-valued irreducible cracovian representations. The covariance of a five-dimensional form of the Dirac equation with respect to the quasi-rotations forming quasigroups connected with the groups SO(4, 1) and SO(3, 2) is demonstrated. An analogy is drawn between Weyl's hidden symmetry group and a quasigroup.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.