The Group of Invertible Elements of the Algebra of Quaternions

Kuzmina, Irina A.   ; Chodorová, Marie

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 55 (2016) no. 1, pp. 53-58

Abstract (VO)

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.

Détail

Classification : 53B20, 53B30, 53C21
Keywords: Group of invertible elements; algebra of quaternions; principal locally trivial bundle; 2-dimensional subalgebras; structural group; unit; Hopf fibration

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