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The Group of Invertible Elements of the Algebra of Quaternions

Irina A. KuzminaMarie Chodorová — 2016

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

We have, that all two-dimensional subspaces of the algebra of quaternions, containing a unit, are 2-dimensional subalgebras isomorphic to the algebra 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.

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