HUNTING FOR THE NEW SYMMETRIES IN CALABI–YAU JUNGLES

Abstract

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 CY d (d≥3) reflexive polyhedra have been studied in detail. These graphs can be naturally obtained in the framework of Universal Calabi–Yau algebra (UCYA) and decoded in an universal way by changing 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.