| Title:
|
Subloops of sedenions (English) |
| Author:
|
Kivunge, Benard M. |
| Author:
|
Smith, Jonathan D. H |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
45 |
| Issue:
|
2 |
| Year:
|
2004 |
| Pages:
|
295-302 |
| . |
| Category:
|
math |
| . |
| Summary:
|
This note investigates sedenion multiplication from the standpoint of loop theory. New two-sided loops are obtained within the version of the sedenions introduced by the second author. Conditions are given for the satisfaction of standard loop-theoretical identities within these loops. (English) |
| Keyword:
|
loop |
| Keyword:
|
left loop |
| Keyword:
|
sedenion |
| Keyword:
|
octonion |
| Keyword:
|
Cayley numbers |
| Keyword:
|
inverse property |
| MSC:
|
17A75 |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1101.20041 |
| idMR:
|
MR2075278 |
| . |
| Date available:
|
2009-05-05T16:45:18Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119459 |
| . |
| Reference:
|
[1] Albert A.A: Studies in Modern Algebra.Prentice-Hall, Englewood Cliffs, NJ, 1963. Zbl 0192.00102, MR 0146228 |
| Reference:
|
[2] Conway J.H., Smith D.A.: On Quaternions and Octonions: Their Geometry and Symmetry.A.K. Peters Ltd., Natick, MA, 2003. MR 1957212 |
| Reference:
|
[3] Ebbinghaus H.-D. {et al.}: Numbers.Springer Verlag, New York, NY, 1991. MR 1415833 |
| Reference:
|
[4] Kinyon M.K.: private communication.. |
| Reference:
|
[5] Pfister A.: Zur Darstellung definiter Funktionen als Summe von Quadraten.Inv. Math. 4 (1967), 229-237. Zbl 0222.10022, MR 0222043 |
| Reference:
|
[6] Smith J.D.H.: Quasigroup representation theory.pp.195-207 in ``Universal Algebra and Quasigroup Theory'', (eds. A. Romanowska and J.D.H. Smith), Heldermann, Berlin, 1992. Zbl 0772.20023, MR 1191234 |
| Reference:
|
[7] Smith J.D.H.: A left loop on the $15$-sphere.J. Algebra 176 (1995), 128-138. Zbl 0841.17004, MR 1345298 |
| Reference:
|
[8] Smith J.D.H., Romanowska A.B.: Post-Modern Algebra.Wiley, New York, NY, 1999. Zbl 0946.00001, MR 1673047 |
| Reference:
|
[9] Taylor W.: Spaces and equations.Fund. Math. 164 (2000), 193-240. Zbl 0968.08004, MR 1784642 |
| Reference:
|
[10] Zassenhaus H., Eichhorn W.: Herleitung von Acht- und Sechzehn-Quadrate-Identitäten mit Hilfe von Eigenschaften der verallgemeinerten Quaternionen und der Cayley-Dicksonschen Zahlen.Arch. Math. 17 (1966), 492-496. Zbl 0145.26301, MR 0206027 |
| . |
