Hunting for the New Symmetries in Calabi-Yau Jungles

TL;DR

This paper explores new symmetries and algebraic structures emerging from Calabi-Yau geometries, particularly through graph analysis of reflexive polyhedra and their relation to generalized Lie and Kac-Moody algebras.

Contribution

It introduces Berger graphs derived from Calabi-Yau reflexive polyhedra and links them to generalized algebraic structures beyond traditional Lie algebras.

Findings

Identification of new Berger graphs from Calabi-Yau geometries

Connection of these graphs to generalized Lie and Kac-Moody algebras

Potential for discovering new symmetries in Calabi-Yau spaces

Abstract

It was proposed that the Calabi-Yau geometry can be intrinsically connected with some new symmetries, some new algebras. In order to do this it has been analyzed the graphs constructed from K3-fibre CY_d (d \geq 3) reflexive polyhedra. The graphs can be naturally get in the frames of Universal Calabi-Yau algebra (UCYA) and may be decode by universal way with changing of some restrictions on the generalized Cartan matrices associated with the Dynkin diagrams that characterize affine Kac-Moody algebras. We propose that these new Berger graphs can be directly connected with the generalizations of Lie and Kac-Moody algebras.