Ternary numbers and algebras. Reflexive numbers and Berger graphs

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dc.creatorDubrovskiy, A.
dc.creatorVolkov, G.
dc.date2006-08-11
dc.date2007-06-11
dc.date.accessioned2026-07-07T11:07:01Z
dc.date.available2026-07-07T11:07:01Z
dc.descriptionThe Calabi-Yau spaces with SU(m) holonomy can be studied by the algebraic way through the integer lattice where one can construct the Newton reflexive polyhedra or the Berger graphs. Our conjecture is that the Berger graphs can be directly related with the $n$-ary algebras. To find such algebras we study the n-ary generalization of the well-known binary norm division algebras, ${\mathbb R}$, ${\mathbb C}$, ${\mathbb H}$, ${\mathbb O}$, which helped to discover the most important "minimal" binary simple Lie groups, U(1), SU(2) and G(2). As the most important example, we consider the case $n=3$, which gives the ternary generalization of quaternions and octonions, $3^p$, $p=2,3$, respectively. The ternary generalization of quaternions is directly related to the new ternary algebra and group which are related to the natural extensions of the binary $su(3)$ algebra and SU(3) group. Using this ternary algebra we found the solution for the Berger graph: a tetrahedron.
dc.descriptionRevised version with minor corrections
dc.identifierhttps://arxiv.org/abs/hep-th/0608073
dc.identifierhttp://arxiv.org/abs/hep-th/0608073
dc.identifierAdv.Appl.CliffordAlgebras17:159-181,2007
dc.identifierdoi:10.1007/s00006-007-0028-9
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/189710
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleTernary numbers and algebras. Reflexive numbers and Berger graphs
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