| Title:
|
Hypercomplex Algebras and Geometry of Spaces with Fundamental Formof an Arbitrary Order (English) |
| Author:
|
Burlakov, Mikhail P. |
| Author:
|
Burlakov, Igor M. |
| Author:
|
Jukl, Marek |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
55 |
| Issue:
|
1 |
| Year:
|
2016 |
| Pages:
|
31-38 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The article is devoted to a generalization of Clifford and Grassmann algebras for the case of vector spaces over the field of complex numbers. The geometric interpretation of such generalizations are presented. Multieuclidean geometry is considered as well as the importance of it in physics. (English) |
| Keyword:
|
Hypercomplex algebras |
| Keyword:
|
geometry of spaces with fundamental form |
| Keyword:
|
Clifford algebras |
| MSC:
|
15A66 |
| MSC:
|
53B30 |
| MSC:
|
57R15 |
| idZBL:
|
Zbl 1367.53014 |
| idMR:
|
MR3674597 |
| . |
| Date available:
|
2016-08-30T11:51:55Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145814 |
| . |
| Reference:
|
[1] Rosenfeld, B. A.: Neevklidovy geometrii.. GITTL, Moscow, 1955, (in Russian). |
| Reference:
|
[2] Burlakov, M. P.: Clifford structures on manifolds.. J. Math. Sci. 89, 3 (1998), 1311–1333, Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 30, Geometriya-3, 1995. Zbl 0930.53030, MR 1619716, 10.1007/BF02414874 |
| Reference:
|
[3] Burlakov, M. P.: Gamiltonovy algebry.. Graf-press, Moscow, 2006, (in Russian). |
| Reference:
|
[4] Chelzen, F., Martin, A.: Kvarki i leptony.. Mir, Moscow, 1987, (in Russian). |
| Reference:
|
[5] Penrouz, R., Rindler, V.: Spinory i prostranstvo-vremja.. Mir, Moscow, 1987, (in Russian). MR 0908073 |
| Reference:
|
[6] Efimov, N. V., Rozendorn, E. R.: Linear algebra and multidimensional geometry.. Nauka, Moscow, 1975, (in Russian). |
| . |
