# Derivations, Gradings, Actions of Algebraic Groups, and Codimension Growth of Polynomial Identities

```@article{Gordienko2012DerivationsGA,
title={Derivations, Gradings, Actions of Algebraic Groups, and Codimension Growth of Polynomial Identities},
author={A. S. Gordienko and M. Kochetov},
journal={Algebras and Representation Theory},
year={2012},
volume={17},
pages={539-563}
}```
• Published 2012
• Mathematics
• Algebras and Representation Theory
Suppose a finite dimensional semisimple Lie algebra \$\mathfrak g\$ acts by derivations on a finite dimensional associative or Lie algebra A over a field of characteristic 0. We prove the \$\mathfrak g\$-invariant analogs of Wedderburn—Mal’cev and Levi theorems, and the analog of Amitsur’s conjecture on asymptotic behavior for codimensions of polynomial identities with derivations of A. It turns out that for associative algebras the differential PI-exponent coincides with the ordinary one. Also we… Expand
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