On identities of infinite dimensional Lie superalgebras
  We study codimension growth of infinite dimensional Lie superalgebras over an algebraically closed field of characteristic zero. We prove that if a Lie superalgebra $L$ is a Grassmann envelope of a finite dimensional simple Lie algebra then the PI-exponent of $L$ exists and it is a positive integer. 
Du\v{s}an Repov\v{s}, Mikhail Zaicev
math.RA