# Ternary Numbers, Algebras of Reflexive Numbers and Berger Graphs

@article{Dubrovski2006TernaryNA,
title={Ternary Numbers, Algebras of Reflexive Numbers and Berger Graphs},
year={2006},
volume={17},
pages={159-181}
}
• Published 11 August 2006
• Mathematics
• Advances in Applied Clifford Algebras
Abstract.The Calabi-Yau spaces with SU(n) 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…
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## References

SHOWING 1-10 OF 22 REFERENCES

It was proposed that the Calabi–Yau geometry can be intrinsically connected with some new symmetries, some new algebras. In order to do so the Berger graphs corresponding to K3-fibre CYd (d≥3)
• Mathematics
• 1987
We present a detailed and complete proof of our earlier conjecture on the classification of minimal conformal invariant theories. This is based on an exhaustive construction of all modular invariant
• S. Yau
• Mathematics
Proceedings of the National Academy of Sciences of the United States of America
• 1977
A proof of Calabi's conjectures on the Ricci curvature of a compact Kähler manifold is announced and some new results in algebraic geometry and differential geometry are proved, including that the only Köhler structure on a complex projective space is the standard one.
We consider families ${\cal F}(\Delta)$ consisting of complex $(n-1)$-dimensional projective algebraic compactifications of $\Delta$-regular affine hypersurfaces $Z_f$ defined by Laurent polynomials
Experimental observation of Majorana fermion matter gives a new impetus to the understanding of the Lorentz symmetry and its extension, the geometrical properties of the ambient space-time structure,
• Mathematics
• 1995
Abstract We define the notion of a "Lie k -algebra" to be a ( k + 1)-ary skew-symmetric operation on a bigraded vector space which satisfies a certain relation of degree 2 k + 1. The notion of Lie
+ {g1, {f1, . . . , fn−1, g2}, g3, . . . , gn} + · · ·+ {g1, . . . , gn−1, {f1, . . . , fn−1, gn}} for all f1, . . . , fn−1, g1, . . . , gn ∈ C∞(M). We should note that (f1, . . . , fn−1) acts on