Subloops of sedenions

Benard M. Kivunge; Jonathan D. H Smith

Commentationes Mathematicae Universitatis Carolinae (2004)

  • Volume: 45, Issue: 2, page 295-302
  • ISSN: 0010-2628

Abstract

top
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.

How to cite

top

Kivunge, Benard M., and Smith, Jonathan D. H. "Subloops of sedenions." Commentationes Mathematicae Universitatis Carolinae 45.2 (2004): 295-302. <http://eudml.org/doc/249331>.

@article{Kivunge2004,
abstract = {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.},
author = {Kivunge, Benard M., Smith, Jonathan D. H},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {loop; left loop; sedenion; octonion; Cayley numbers; inverse property; left loops; sedenions; octonions; Cayley numbers; inverse property loops},
language = {eng},
number = {2},
pages = {295-302},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Subloops of sedenions},
url = {http://eudml.org/doc/249331},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Kivunge, Benard M.
AU - Smith, Jonathan D. H
TI - Subloops of sedenions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 2
SP - 295
EP - 302
AB - 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.
LA - eng
KW - loop; left loop; sedenion; octonion; Cayley numbers; inverse property; left loops; sedenions; octonions; Cayley numbers; inverse property loops
UR - http://eudml.org/doc/249331
ER -

References

top
  1. Albert A.A, Studies in Modern Algebra, Prentice-Hall, Englewood Cliffs, NJ, 1963. Zbl0192.00102MR0146228
  2. Conway J.H., Smith D.A., On Quaternions and Octonions: Their Geometry and Symmetry, A.K. Peters Ltd., Natick, MA, 2003. MR1957212
  3. Ebbinghaus H.-D. {et al.}, Numbers, Springer Verlag, New York, NY, 1991. MR1415833
  4. Kinyon M.K., private communication, . 
  5. Pfister A., Zur Darstellung definiter Funktionen als Summe von Quadraten, Inv. Math. 4 (1967), 229-237. (1967) Zbl0222.10022MR0222043
  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. Zbl0772.20023MR1191234
  7. Smith J.D.H., A left loop on the 15 -sphere, J. Algebra 176 (1995), 128-138. (1995) Zbl0841.17004MR1345298
  8. Smith J.D.H., Romanowska A.B., Post-Modern Algebra, Wiley, New York, NY, 1999. Zbl0946.00001MR1673047
  9. Taylor W., Spaces and equations, Fund. Math. 164 (2000), 193-240. (2000) Zbl0968.08004MR1784642
  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. (1966) Zbl0145.26301MR0206027

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.