2009

The Split-Algebras and Non-compact Hopf Maps

Hasebe, Kazuki

Understand

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.

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Cited in the paper.
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Cited in the paper.

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2003
Later among the works it cites.
See for instance, John C. Baez, “The Octonions”
2005
Later among the works it cites.
Kazuki Hasebe, Yusuke Kimura, “Fuzzy Supersphere and Supermonopole”
2005
Later among the works it cites.
Giovanni Landi, Chiara Pagani, Cesare Reina, “A Hopf bundle over a quantum four-sphere from the symplectic group”
2006
Later among the works it cites.
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2006
Later among the works it cites.
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2007
Later among the works it cites.
Kazuki Hasebe, “Hyperbolic Supersymmetric Quantum Hall Effect”
Original
2008
Later among the works it cites.
M. Gonzales, Z. Kuznetsova, A. Nersessian, F. Toppan, V. Yeghikyan, “Second Hopf map and supersymmetric mechanics with Yang monopole”
Original
2009
Closest in time.
Kazuki Hasebe, “Split-Quaternionic Hopf Map, Quantum Hall Effect, and Twistor Theory”
Original
2010
Closest in time.

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