Octonion multiplication and Heawood’s map
Confluentes Mathematici, Volume 5 (2013) no. 2, p. 71-76

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.

DOI : https://doi.org/10.5802/cml.9
Classification:  17A35,  05C10,  05C25
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author = {S\'evennec, Bruno},
title = {Octonion multiplication and Heawood's map},
journal = {Confluentes Mathematici},
publisher = {Institut Camille Jordan},
volume = {5},
number = {2},
year = {2013},
pages = {71-76},
doi = {10.5802/cml.9},
mrnumber = {3145034},
language = {en},
url = {http://www.numdam.org/item/CML_2013__5_2_71_0}
}

Sévennec, Bruno. Octonion multiplication and Heawood’s map. Confluentes Mathematici, Volume 5 (2013) no. 2, pp. 71-76. doi : 10.5802/cml.9. http://www.numdam.org/item/CML_2013__5_2_71_0/

[1] J. C. Baez. The octonions. Bull. Amer. Math. Soc., 39:145–205, 2002. | MR 1886087 | Zbl 1026.17001

[2] B. Bollobas. Modern graph theory., Graduate Texts in Mathematics, Vol. 184. Springer-Verlag, New York-Berlin, 1998. | MR 1633290 | Zbl 0902.05016

[3] E. Brown and N. Loehr. Why is PSL(2,7) $\simeq$ GL(3,2)?. Amer. Math. Monthly 116:727–731, 2009. | MR 2572107 | Zbl 1229.20046

[4] J. H. Conway and D. A. Smith. Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry. AK Peters, 2003. | MR 1957212 | Zbl 1098.17001

[5] R. L. Griess Jr. Sporadic groups, code loops and nonvanishing cohomology. J. Pure Appl. Algebra, 44:191–214, 1987. | MR 885104 | Zbl 0611.20009

[6] P. J. Heawood. Map colour theorem. Quart. J. Pure Appl. Math., 24:332–338, 1980.

[7] D. R. Hughes and F. C. Piper. Projective planes, Graduate Texts in Mathematics, Vol. 6. Springer-Verlag, New York-Berlin, 1973. | MR 333959 | Zbl 0267.50018

[8] J. H. van Lint and R. M. Wilson. A course in combinatorics, Second edition. Cambridge University Press, Cambridge, 2001. | MR 1871828 | Zbl 0769.05001

[9] L. Manivel. Configurations of lines and models of Lie algebras. J. Algebra 304:457–486, 2006. | MR 2256401 | Zbl 1167.17001