A note on semisimple derivations of commutative algebras
Volume 102 / 2005
Colloquium Mathematicum 102 (2005), 263-270
MSC: 13A02, 13B10, 14L30.
DOI: 10.4064/cm102-2-7
Abstract
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 $\mathop {\rm Max}\nolimits (A)$, and, using this, that in some cases the derivation $d$ is linearizable or admits a maximal invariant ideal.
