The above article originally published with errors. The errors and corrected text are detailed here:

On page 5:

“If g is a restricted Lie algebra, there is a six-term exact sequence [3.2, 18] that relates the ordinary and restricted 1- and 2-cohomology spaces:” should read:

“If g is a restricted Lie algebra, there is a six-term exact sequence [11, 18] that relates the ordinary and restricted 1- and 2-cohomology spaces:”.

On page 7:

“If q = 1 or q = 2, then the second term in part (2) of Lemma 11.11 vanishes,” should read:

“If q = 1 or q = 2, then the second term in part (2) of Lemma 3.2 vanishes,”.

On page 8:

“For any restricted Lie algebra g, [11.11, Theorem 2.1] states that” should read:

“For any restricted Lie algebra g, [11, Theorem 2.1] states that”.

On page 9:

1. 1. ‘restricted one-dimensional central extensions of a restricted Lie algebra g are parameterized by the restricted cohomology group $H^2_*(\mathfrak g)$ [[11.11], Theorem 3.3].’ should read:

   ‘restricted one-dimensional central extensions of a restricted Lie algebra g are parameterized by the restricted cohomology group $H^2_*(\mathfrak g)$ [11, Theorem 3.3].’.

1. 2. “We can the equations (9) together with Theorem 5.1 to explicitly describe the restricted one-dimensional central extensions” should read:

   “We can use the equations (9) together with Theorem 5.1 to explicitly describe the restricted one-dimensional central extensions”.

On page 12:

1. 1. Reference 17:

   “H. Strade and R. Farnsteiner. Modular Lie algebras and their representations. Monographs and Textbooks in Pure and Applied Math. Vol. 116, (Marcel Dekker, Inc, New York, 1988).” should read:

   “H. Strade and R. Farnsteiner. Modular Lie algebras and their representations. Monographs and Textbooks in Pure and Applied Math. Vol. 116, Marcel Dekker, Inc, New York, 1988.”

1. 2. Reference 18:

   “F. Viviani. Restricted infinitesimal deformations of restricted simple Lie algebras. J. Algebra Appl. 11 “(2012), 19.’ should read:

   “F. Viviani. Restricted infinitesimal deformations of restricted simple Lie algebras. J. Algebra Appl. 11 (2012), 19 pp.”