Codimensions of polynomial identities of representations of Lie algebras

Abstract

Consider a representation $\rho :L\to \mathfrak{gl}(V)$ where $L$ is a Lie algebra and $V$ is a finite dimensional vector space. We prove the analog of Amitsur's conjecture on asymptotic behavior for codimensions of polynomial identities of $\rho$.

arXiv comment12 pages. Lemma 11 and Lemma 12 were clarified. Also some other minor misprints has been corrected. Examples 1-5 were added