Construction of the Outer Automorphism of $${\mathcal {S}}_{6}$$ S 6 via a Complex Hadamard Matrix

We give a new construction of the outer automorphism of the symmetric group on six points. Our construction features a complex Hadamard matrix of order six containing third roots of unity and the algebra of split quaternions over the real numbers.

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Bibliographic Details
Published in:Mathematics in computer science 2018-12, Vol.12 (4), p.453-458
Main Authors: Gillespie, Neil I., Ó Catháin, Padraig, Praeger, Cheryl E.
Format: Article
Language:English
Subjects:
Automorphisms
Matrices (mathematics)
Quaternions
Real numbers
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Description
Summary:We give a new construction of the outer automorphism of the symmetric group on six points. Our construction features a complex Hadamard matrix of order six containing third roots of unity and the algebra of split quaternions over the real numbers.
ISSN:1661-8270
1661-8289
DOI:10.1007/s11786-018-0382-0