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.
Citation
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
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