Journal of Lie Theory

no. 4
Toroidal Affine Nash Groups
Journal of Lie Theory, Volume 26 (2016) no. 4, pp. 1069-1077
A toroidal affine Nash group is the affine Nash group analogue of an anti-affine algebraic group. In this note, we prove analogues of Rosenlicht's structure and decomposition theorems: (1) Every affine Nash group $G$ has a smallest normal affine Nash subgroup $H$ such that $G/H$ is an almost linear affine Nash group, and this $H$ is toroidal. (2) If $G$ is a connected affine Nash group, then there exist a largest toroidal affine Nash subgroup $G_{\rm ant}$ and a largest connected, normal, almost linear affine Nash subgroup $G_{\rm aff}$. Moreover, we have $G=G_{\rm ant}G_{\rm aff}$, and $G_{\rm ant}\cap G_{\rm aff}$ contains $(G_{\rm ant})_{\rm aff}$ as an affine Nash subgroup of finite index.
DOI: 10.5802/jolt.923
Classification: 22E15, 14L10, 14P20
Keywords: Real algebraic groups, anti-affine algebraic groups, Rosenlicht's theorem, affine Nash groups, abelian groups 
@article{JOLT_2016_26_4_a5,
     author = {M. B. Can},
     title = {Toroidal {Affine} {Nash} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {1069--1077},
     year = {2016},
     volume = {26},
     number = {4},
     doi = {10.5802/jolt.923},
     zbl = {1354.22011},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.923/}
}
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M. B. Can. Toroidal Affine Nash Groups. Journal of Lie Theory, Volume 26 (2016) no. 4, pp. 1069-1077. doi: 10.5802/jolt.923

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