Abstract
We develop a noncompact version of the Hopf maps based on the split algebras. The split algebras consist of three species: split-complex numbers, split quaternions, and split octonions. They correspond to three noncompact Hopf maps that represent topological maps between hyperboloids in different dimensions with hyperboloid bundle. We realize such noncompact Hopf maps in two ways: one is to utilize the split-imaginary unit, and the other is to utilize the ordinary imaginary unit. Topological structures of the hyperboloid bundles are explored, and the canonical connections are naturally regarded as noncompact gauge field of monopoles.
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.