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A 2X2 Matrix Approach to Hopf Fibrations:: Quaternionic Reduction of Octonionic Bi-unitary Matrices and an RLLR/LRRL Bracketing Rule
We develop a common two-by-two matrix framework for the four classical Hopf fibrations associated with the real, complex, quaternionic and octonionic numbers. In all four cases the Hopf map is the image of the north pole of a sphere of trace-free Hermitian matrices under conjugation by a bi-unitary
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