Codimension growth of central polynomials of Lie algebras

Abstract

Abstract Let L be a finite-dimensional simple Lie algebra over an algebraically closed field of characteristic zero and let I be the T-ideal of polynomial identities of the adjoint representation of L. We prove that the number of multilinear central polynomials in n variables, linearly independent modulo I, grows exponentially like ( dim ⁡ L ) n {(\dim L)^{n}} .