Universal transitivity of simple and 2-simple prehomogeneous vector spaces

Kimura, T., Kasai, S., and Hosokawa, H.. "Universal transitivity of simple and 2-simple prehomogeneous vector spaces." Annales de l'institut Fourier 38.2 (1988): 11-41. <http://eudml.org/doc/74797>.

@article{Kimura1988,
abstract = {We denote by $k$ a field of characteristic zero satisfying $H^ 1(k,\{\rm Aut\}(SL_ 2))\ne 0$. Let $G$ be a connected $k$-split linear algebraic group acting on $X=\{\rm Aff\}^ n$ rationally by $\rho $ with a Zariski-dense $G$-orbit $Y$. A prehomogeneous vector space $(G,\rho $,X) is called “universally transitive” if the set of $k$-rational points $Y(k)$ is a single $\rho $$(G)(k)$-orbit for all such $k$. Such prehomogeneous vector spaces are classified by J. Igusa when $\rho $ is irreducible. We classify them when $G$ is reductive and its commutator subgroup $[G,G]$ is either a simple algebraic group or a product of two simple algebraic groups.},
author = {Kimura, T., Kasai, S., Hosokawa, H.},
journal = {Annales de l'institut Fourier},
keywords = {prehomogeneous vector spaces; Galois cohomology},
language = {eng},
number = {2},
pages = {11-41},
publisher = {Association des Annales de l'Institut Fourier},
title = {Universal transitivity of simple and 2-simple prehomogeneous vector spaces},
url = {http://eudml.org/doc/74797},
volume = {38},
year = {1988},
}

TY - JOUR
AU - Kimura, T.
AU - Kasai, S.
AU - Hosokawa, H.
TI - Universal transitivity of simple and 2-simple prehomogeneous vector spaces
JO - Annales de l'institut Fourier
PY - 1988
PB - Association des Annales de l'Institut Fourier
VL - 38
IS - 2
SP - 11
EP - 41
AB - We denote by $k$ a field of characteristic zero satisfying $H^ 1(k,{\rm Aut}(SL_ 2))\ne 0$. Let $G$ be a connected $k$-split linear algebraic group acting on $X={\rm Aff}^ n$ rationally by $\rho $ with a Zariski-dense $G$-orbit $Y$. A prehomogeneous vector space $(G,\rho $,X) is called “universally transitive” if the set of $k$-rational points $Y(k)$ is a single $\rho $$(G)(k)$-orbit for all such $k$. Such prehomogeneous vector spaces are classified by J. Igusa when $\rho $ is irreducible. We classify them when $G$ is reductive and its commutator subgroup $[G,G]$ is either a simple algebraic group or a product of two simple algebraic groups.
LA - eng
KW - prehomogeneous vector spaces; Galois cohomology
UR - http://eudml.org/doc/74797
ER -