't Hooft's solution for arbitrary semisimple Lie group

The generalization of the 't Hooft's A1 solution for every semisimple Lie algebra is found. The solution depends on r-independent chains of linear self-dual systems (Δsα)z = (Δs+1α)y-bar, (Δsα)y-bar = -(Δs+1α)z (1 ≤ α ≤ r); the length of α chain is equal to 2ωα + 1, where ωα are the indexes of the semisimple algebra and r is its rank. In the special case the O(4)-invariant solutions with instanton number equal to one arises. (author). 6 refs