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Integral Octonions, Octonion XY-Product, and the Leech Lattice
Integral Octonions Octonion XY-Product
2010/12/23
The integral octonions arise from the octonion XY-product. A parallel is shown to exist with the quaternion Z-product. Connections to the laminated lattices, $\Lambda_{4}$, $\Lambda_{8}$, $\Lambda_{16...
We present a generalization of the construction of graphs by Lubotzky, Phillips and Sarnak in their celebrated article "Ramanujan graphs". The new approach consists in using octonion algebras rather ...
Weyl groups of fine gradings on matrix algebras, octonions and the Albert algebra
Graded algebra fine grading Weyl group octonions Albert algebra
2010/12/1
Given a grading : A = Lg2G Ag on a nonassociative algebra A by an abelian group G.
Rotations in the Space of Split Octonions
Nonassociative algebras Rotations Split Octonions
2009/9/4
The geometrical application of split octonions is considered. The new representation of products of the basis units of split octonionic having David's star shape (instead of the Fano triangle) is pres...