The Group of Invertible Elements of the Algebra of Quaternions

Irina A. Kuzmina; Marie Chodorová

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2016)

  • Volume: 55, Issue: 1, page 53-58
  • ISSN: 0231-9721

Abstract

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

How to cite

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Kuzmina, Irina A., and Chodorová, Marie. "The Group of Invertible Elements of the Algebra of Quaternions." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 55.1 (2016): 53-58. <http://eudml.org/doc/286705>.

@article{Kuzmina2016,
abstract = {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.},
author = {Kuzmina, Irina A., Chodorová, Marie},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Group of invertible elements; algebra of quaternions; principal locally trivial bundle; 2-dimensional subalgebras; structural group; unit; Hopf fibration},
language = {eng},
number = {1},
pages = {53-58},
publisher = {Palacký University Olomouc},
title = {The Group of Invertible Elements of the Algebra of Quaternions},
url = {http://eudml.org/doc/286705},
volume = {55},
year = {2016},
}

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
PB - Palacký University Olomouc
VL - 55
IS - 1
SP - 53
EP - 58
AB - 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.
LA - eng
KW - Group of invertible elements; algebra of quaternions; principal locally trivial bundle; 2-dimensional subalgebras; structural group; unit; Hopf fibration
UR - http://eudml.org/doc/286705
ER -

References

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