Geodesic
The Group of Invertible Elements of the Algebra of Quaternions
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 55 (2016) no. 1, pp. 53-58 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 53B20, 53B30, 53C21
Keywords: Group of invertible elements; algebra of quaternions; principal locally trivial bundle; 2-dimensional subalgebras; structural group; unit; Hopf fibration 
@article{AUPO_2016_55_1_a7,
     author = {Kuzmina, Irina~A. and Chodorov\'a, Marie},
     title = {The {Group} of {Invertible} {Elements} of the {Algebra} of {Quaternions}},
     journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
     pages = {53--58},
     year = {2016},
     volume = {55},
     number = {1},
     mrnumber = {3674600},
     zbl = {1362.16024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUPO_2016_55_1_a7/}
}
TY  - JOUR
AU  - Kuzmina, Irina A.
AU  - Chodorová, Marie
TI  - The Group of Invertible Elements of the Algebra of Quaternions
JO  - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY  - 2016
SP  - 53
EP  - 58
VL  - 55
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/AUPO_2016_55_1_a7/
LA  - en
ID  - AUPO_2016_55_1_a7
ER  - 
%0 Journal Article
%A Kuzmina, Irina A.
%A Chodorová, Marie
%T The Group of Invertible Elements of the Algebra of Quaternions
%J Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
%D 2016
%P 53-58
%V 55
%N 1
%U http://geodesic.mathdoc.fr/item/AUPO_2016_55_1_a7/
%G en
%F AUPO_2016_55_1_a7
Kuzmina, Irina A.; Chodorová, Marie. The Group of Invertible Elements of the Algebra of Quaternions. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 55 (2016) no. 1, pp. 53-58. http://geodesic.mathdoc.fr/item/AUPO_2016_55_1_a7/