English

Generalized Cartan-Kac Matrices inspired from Calabi-Yau spaces

High Energy Physics - Theory 2026-05-21 v2

Abstract

The object of this work is the systematical study of a certain type of generalized Cartan matrices associated with the Dynkin diagrams that characterize Cartan-Lie and affine Kac-Moody algebras. These generalized matrices are associated to graphs which arise in the study and classification of Calabi-Yau spaces through Toric Geometry. We focus in the study of what should be considered the generalization of the affine exceptional series E6,7,8(1)E_{6,7,8}^{(1)} Kac-Moody matrices. It has been conjectured that these generalized simply laced graphs and associated link matrices may characterize generalizations of Cartan-Lie and affine Kac-Moody algebras.

Keywords

Cite

@article{arxiv.hep-th/0503151,
  title  = {Generalized Cartan-Kac Matrices inspired from Calabi-Yau spaces},
  author = {E. Torrente-Lujan},
  journal= {arXiv preprint arXiv:hep-th/0503151},
  year   = {2026}
}