| 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:
|
http://hdl.handle.net/10338.dmlcz/145817 |
| . |
| Reference:
|
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| Reference:
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