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Title: The Group of Invertible Elements of the Algebra of Quaternions (English)
Author: Kuzmina, Irina A.
Author: Chodorová, Marie
Language: English
Journal: Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
ISSN: 0231-9721
Volume: 55
Issue: 1
Year: 2016
Pages: 53-58
Summary lang: English
Category: math
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. (English)
Keyword: Group of invertible elements
Keyword: algebra of quaternions
Keyword: principal locally trivial bundle
Keyword: 2-dimensional subalgebras
Keyword: structural group
Keyword: unit
Keyword: Hopf fibration
MSC: 53B20
MSC: 53B30
MSC: 53C21
idZBL: Zbl 1362.16024
idMR: MR3674600
Date available: 2016-08-30T11:55:03Z
Last updated: 2018-01-10
Stable URL:
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