Graded Lie algebras and regular prehomogeneous vector spaces with one-dimensional scalar multiplication

Abstract

The aim of this paper is to study relations between regular reductive PVs with one-dimensional scalar multiplication and the structure of graded Lie algebras. We will show that the regularity of such PVs is described by an ${\mathfrak{sl}}_2$-triplet of a graded Lie algebra.

References in corpus (4)

• Lie algebras constructed with Lie modules and their positively and negatively graded modules
• Fabricating Highly Ordered Nanofiber Assemblies by Controlled Shear Flow and Solvent Evaporation
• Contragredient Lie algebras and Lie algebras associated with a standard pentad
• Reduced contragredient Lie algebras and PC Lie algebras