The axioms depend on the signs of the generators, which are specified by lieAlgebra(..., genSigns => ...). The sign of an element can be obtained by the function signLie, in the axioms below the sign of an element a is written sign(a).
Anticommutativity: [a,b] = -(-1)sign(a) * sign(b) [b,a]
Jacobi identity: [a,[b,c]] = [[a,b],c] + (-1)sign(a) * sign(b) [b,[a,c]]
Also, in characteristic 2 and 3, there are in addition the following axioms:
Characteristic 2: [a,a] = 0
Characteristic 3: [a,[a,a]] = 0