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 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}
}