A concept of a slice of a semisimple derivation is introduced. Moreover, it is shown that a semisimple derivation d of a finitely generated commutative algebra A over an algebraically closed field of characteristic 0 is nothing other than an algebraic action of a torus on Max(A), and, using this, that in some cases the derivation d is linearizable or admits a maximal invariant ideal.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm102-2-7,
author = {Andrzej Tyc},
title = {A note on semisimple derivations of commutative algebras},
journal = {Colloquium Mathematicae},
volume = {103},
year = {2005},
pages = {263-270},
zbl = {1115.13034},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm102-2-7}
}
Andrzej Tyc. A note on semisimple derivations of commutative algebras. Colloquium Mathematicae, Tome 103 (2005) pp. 263-270. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm102-2-7/