2004/06/03 by E. Torrente-Lujan, E. Torrente-Luján, Torrente-Lujan, E. +3 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Geometry and complex manifolds #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0406035
24 pages, 6 figures
arxiv created 2004/06/03 · arxiv updated 2009/12/01
The algebraic approach to the construction of the reflexive polyhedra that yield Calabi-Yau spaces in three or more complex dimensions with K3 fibres reveals graphs that include and generalize the Dynkin diagrams associated with gauge symmetries. In this work we continue to study the structure of graphs obtained from CY3 reflexive polyhedra. We show how some particularly defined integral matrices can be assigned to these diagrams. This family of matrices and its associated graphs may be obtained by relaxing the restrictions on the individual entries of the generalized Cartan matrices associated with the Dynkin diagrams that characterize Cartan-Lie and affine Kac-Moody algebras. These graphs keep however the affine structure, as it was in Kac-Moody Dynkin diagrams. We presented a possible root structure for some simple cases. We conjecture that these generalized graphs and associated link matrices may characterize generalizations of these algebras.