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

2017/04/08 by Nagatoshi Sasano, Sasano, Nagatoshi
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1704.02460

openalex publication_date 2017/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \mathfraksl₂-triplet of a graded Lie algebra.

Citations

• 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

Related

• Reduced contragredient Lie algebras and PC Lie algebras
• Structure constants for simple Lie algebras from principal \mathfraksl₂-triple
• Graded Lie algebras of type FP
• Classification of some simple graded pre-Lie algebras of growth one
• The Levi Decomposition of a Graded Lie Algebra