Derivations and central extensions of simple modular Lie algebras and superalgebras

Over algebraically closed fields of positive characteristic, we list the outer derivations and non-trivial central extensions of simple finite dimensional Lie algebras and Lie superalgebras of the rank sufficiently small to allow computer-aided study using Mathematica-based code SuperLie. We consider algebras possessing a grading by integers such that the dimensions of the superspaces whose degrees are equal in absolute value coincide (symmetric algebras), and also non-trivial deforms of these algebras. When the answer is clear for the infinite series, it is given for any rank. We also consider the non-symmetric case of periplectic Lie superalgebras and the Lie algebras obtained from them by desuperization.