RADICAL

PASCAL programs for identification of Lie algebras. I: RADICAL - a program to calculate the radical and nil radical of parameter-free and parameter-dependent Lie algebras. The program RADICAL (based on PASCAL) presented by the author is a package of 127 subprograms (5300 lines) and determines for a Lie algebra L given by its structure constants (which can be either integers or polynomials) the radical or the nilradical, respectively. Radicals are calculated as orthogonal complement (with respect to the Killing form) of the derived Lie algebra [L,L], that means by solution of a system of linear homogeneous equations. For the determination of nilradicals a new algorithm is used without any irrational calculations. The program has been successfully tested with Lie algebras of dimensions up to 30. For $dim =5$ one has running times of few seconds (on CDC- CYBER-Computer). Various examples are given. For theoretical foundations see Zbl 0668.17004. (Some essential modifications are given in the erratum notice.)

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