| Title:
|
Note on analytic Moufang loops (English) |
| Author:
|
Paal, Eugen |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
45 |
| Issue:
|
2 |
| Year:
|
2004 |
| Pages:
|
349-354 |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is explicitly shown how the Lie algebras can be associated with the analytic Moufang loops. The resulting Lie algebra commutation relations are well known from the theory of alternative algebras. (English) |
| Keyword:
|
Moufang loop |
| Keyword:
|
Mal'tsev algebra |
| Keyword:
|
generalized Maurer-Cartan equations |
| Keyword:
|
triality |
| MSC:
|
17D10 |
| MSC:
|
20N05 |
| MSC:
|
22A30 |
| idZBL:
|
Zbl 1099.22004 |
| idMR:
|
MR2075282 |
| . |
| Date available:
|
2009-05-05T16:45:40Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119463 |
| . |
| Reference:
|
[1] Moufang R.: Zur Struktur von Alternativkörpern.Math. Ann. B110 (1935), 416-430. MR 1512948 |
| Reference:
|
[2] Pflugfelder H.: Quasigroups and Loops: Introduction.Heldermann Verlag Berlin (1990). Zbl 0715.20043, MR 1125767 |
| Reference:
|
[3] Mal'tsev A.I.: Analytic loops.Matem. Sb. 36 (1955), 569-576 (in Russian). MR 0069190 |
| Reference:
|
[4] Paal E.: An Introduction to Moufang Symmetry.Preprint F-42 Institute of Physics, Tartu (1987 (in Russian)). MR 1241991 |
| Reference:
|
[5] Loos O.: Über eine Beziehung zwischen Malcev-Algebren und Lie-Tripelsystemen.Pacific J. Math. 18 (1966), 553-562. Zbl 0145.04202, MR 0199236 |
| Reference:
|
[6] Yamaguti K.: Note on Malcev algebras.Kumamoto J. Sci. A5 (1962), 203-207. Zbl 0166.04203, MR 0158911 |
| Reference:
|
[7] Yamaguti Y.: On the theory of Malcev algebras.Kumamoto J. Sci. A6 (1963), 9-45. Zbl 0138.26203, MR 0167507 |
| Reference:
|
[8] Schafer R.D.: An Introduction to Nonassociative Algebras.Academic Press New York (1966). Zbl 0145.25601, MR 0210757 |
| . |
