Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-08-11
Adv.Appl.CliffordAlgebras17:159-181,2007
Physics
High Energy Physics
High Energy Physics - Theory
Revised version with minor corrections
Scientific paper
10.1007/s00006-007-0028-9
The 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.
Dubrovskiy A. A.
Volkov Gennady
No associations
LandOfFree
Ternary numbers and algebras. Reflexive numbers and Berger graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Ternary numbers and algebras. Reflexive numbers and Berger graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ternary numbers and algebras. Reflexive numbers and Berger graphs will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-546997