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December 2017 Graded Lie algebras and regular prehomogeneous vector spaces with one-dimensional scalar multiplication
Nagatoshi Sasano
Proc. Japan Acad. Ser. A Math. Sci. 93(10): 124-128 (December 2017). DOI: 10.3792/pjaa.93.124

Abstract

The aim of this paper is to study relations between regular reductive prehomogeneous vector spaces (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.

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Nagatoshi Sasano. "Graded Lie algebras and regular prehomogeneous vector spaces with one-dimensional scalar multiplication." Proc. Japan Acad. Ser. A Math. Sci. 93 (10) 124 - 128, December 2017. https://doi.org/10.3792/pjaa.93.124

Information

Published: December 2017
First available in Project Euclid: 30 November 2017

zbMATH: 06850987
MathSciNet: MR3732902
Digital Object Identifier: 10.3792/pjaa.93.124

Subjects:
Primary: 11S90
Secondary: 17B65 , 17B70

Keywords: graded Lie algebras , prehomogeneous vector spaces , standard pentads

Rights: Copyright © 2017 The Japan Academy

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Vol.93 • No. 10 • December 2017
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