PASCAL programs for identification of Lie algebras. III: Levi decomposition and canonical basis. These are the last parts of a program package based on PASCAL for the identification of a Lie algebra L (given by its structure constants) by computer means. The program LEVI (5100 lines) calculates by a recursive algorithm the semisimple part S(L), of L, together with the radical R(L) (determined by RADICAL, a program presented earlier) there is then realized a Levi decomposition of L. The program CANONIK (10300 lines) uses the parts RADICAL, SPLIT (also presented earlier) and LEVI to present a given Lie algebra with a standardized basis and gives possibilities for its comparison with other Lie algebras. Examples of Lie algebras with canonical bases of dim=10 are given, for the theory of applied algorithms see also Zbl 0668.17004. With respect to the examples and informations the whole package presented by the authors seems to be very effective and useful
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- Rand, D. W.: PASCAL programs for identification of Lie algebras. III: Levi decomposition and canonical basis (1987)