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 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.

29 pages, 15 figures

References in corpus (2)

• Universal Calabi-Yau Algebra: Towards an Unification of Complex Geometry
• Universal Calabi-Yau Algebra: Classification and Enumeration of Fibrations

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