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Keywords:
Group of invertible elements; algebra of quaternions; principal locally trivial bundle; 2-dimensional subalgebras; structural group; unit; Hopf fibration
Group of invertible elements; algebra of quaternions; principal locally trivial bundle; 2-dimensional subalgebras; structural group; unit; Hopf fibration
Summary:
We have, that all two-dimensional subspaces of the algebra of quaternions, containing a unit, are 2-dimensional subalgebras isomorphic to the algebra $\mathbb{C}$ of complex numbers. It was proved in the papers of N. E. Belova. In the present article we consider a 2-dimensional subalgebra $(i)$ of complex numbers with basis ${1, i}$ and we construct the principal locally trivial bundle which is isomorphic to the Hopf fibration.
References:
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