Commutators in classical Lie algebras (Q750582)

The author shows that if a field K has enough elements or if its characteristic is suitably restricted, then for a given element A of a perfect classical Lie algebra \({\mathcal L}\) it is possible to compute in polynomial time X,Y\(\in {\mathcal L}\) such that \(A=[X,Y]\). For these algebras his results differ from those of the reviewer [Proc. Am. Math. Soc. 14, 763-767 (1963; Zbl 0135.073)] by giving, in most cases, a better lower bound for the number of elements in K, and employing a matrix-theoretical proof from which algorithms for the computation of X and Y can be derived.