Pauli gradings on Lie superalgebras and graded codimension growth

We introduce grading on certain finite dimensional simple Lie superalgebras of type P(t) by elementary abelian 2-group. This grading gives rise to Pauli matrices and is a far generalization of (Z2×Z2)-grading on Lie algebra of (2×2)-traceless matrices.We use this grading for studying numerical invariants of polynomial identities of Lie superalgebras. In particular, we compute graded PI-exponent corresponding to Pauli grading.