On the codimension growth of almost nilpotent Lie algebras
  We study codimension growth of infinite dimensional Lie algebras over a field of characteristic zero. We prove that if a Lie algebra $L$ is an extension of a nilpotent algebra by a finite dimensional semisimple algebra then the PI-exponent of $L$ exists and is a positive integer. 
Du\v{s}an Repov\v{s}, Mikhail Zaicev
math.RA