Octonion multiplication and Heawood’s map

Bruno Sévennec[1]

  • [1] UMPA, ENS-Lyon, CNRS, 46 Allée d’Italie, 69364 Lyon cedex 07, France.

Confluentes Mathematici (2013)

  • Volume: 5, Issue: 2, page 71-76
  • ISSN: 1793-7434

Abstract

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In this note, the octonion multiplication table is recovered from a regular tesselation of the equilateral two timensional torus by seven hexagons, also known as Heawood’s map.

How to cite

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Sévennec, Bruno. "Octonion multiplication and Heawood’s map." Confluentes Mathematici 5.2 (2013): 71-76. <http://eudml.org/doc/275424>.

@article{Sévennec2013,
abstract = {In this note, the octonion multiplication table is recovered from a regular tesselation of the equilateral two timensional torus by seven hexagons, also known as Heawood’s map.},
affiliation = {UMPA, ENS-Lyon, CNRS, 46 Allée d’Italie, 69364 Lyon cedex 07, France.},
author = {Sévennec, Bruno},
journal = {Confluentes Mathematici},
language = {eng},
number = {2},
pages = {71-76},
publisher = {Institut Camille Jordan},
title = {Octonion multiplication and Heawood’s map},
url = {http://eudml.org/doc/275424},
volume = {5},
year = {2013},
}

TY - JOUR
AU - Sévennec, Bruno
TI - Octonion multiplication and Heawood’s map
JO - Confluentes Mathematici
PY - 2013
PB - Institut Camille Jordan
VL - 5
IS - 2
SP - 71
EP - 76
AB - In this note, the octonion multiplication table is recovered from a regular tesselation of the equilateral two timensional torus by seven hexagons, also known as Heawood’s map.
LA - eng
UR - http://eudml.org/doc/275424
ER -

References

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  1. J. C. Baez. The octonions. Bull. Amer. Math. Soc., 39:145–205, 2002. Zbl1026.17001MR1886087
  2. B. Bollobas. Modern graph theory., Graduate Texts in Mathematics, Vol. 184. Springer-Verlag, New York-Berlin, 1998. Zbl0902.05016MR1633290
  3. E. Brown and N. Loehr. Why is PSL(2,7) ≃ GL(3,2)?. Amer. Math. Monthly 116:727–731, 2009. Zbl1229.20046MR2572107
  4. J. H. Conway and D. A. Smith. Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry. AK Peters, 2003. Zbl1098.17001MR1957212
  5. R. L. Griess Jr. Sporadic groups, code loops and nonvanishing cohomology. J. Pure Appl. Algebra, 44:191–214, 1987. Zbl0611.20009MR885104
  6. P. J. Heawood. Map colour theorem. Quart. J. Pure Appl. Math., 24:332–338, 1980. Zbl22.0562.02
  7. D. R. Hughes and F. C. Piper. Projective planes, Graduate Texts in Mathematics, Vol. 6. Springer-Verlag, New York-Berlin, 1973. Zbl0267.50018MR333959
  8. J. H. van Lint and R. M. Wilson. A course in combinatorics, Second edition. Cambridge University Press, Cambridge, 2001. Zbl0769.05001MR1871828
  9. L. Manivel. Configurations of lines and models of Lie algebras. J. Algebra 304:457–486, 2006. Zbl1167.17001MR2256401

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