## Proceedings of the Japan Academy, Series A, Mathematical Sciences

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

Nagatoshi Sasano

#### 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.

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 93, Number 10 (2017), 124-128.

Dates
First available in Project Euclid: 30 November 2017

https://projecteuclid.org/euclid.pja/1512032606

Digital Object Identifier
doi:10.3792/pjaa.93.124

Mathematical Reviews number (MathSciNet)
MR3732902

Zentralblatt MATH identifier
06850987

#### Citation

Sasano, Nagatoshi. Graded Lie algebras and regular prehomogeneous vector spaces with one-dimensional scalar multiplication. Proc. Japan Acad. Ser. A Math. Sci. 93 (2017), no. 10, 124--128. doi:10.3792/pjaa.93.124. https://projecteuclid.org/euclid.pja/1512032606

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