On the Identification of a Lie Algebra Given by its Structure Constants

Abstract Methods are given for identifying a Lie algebra L , given by its structure constants. The identification involves a transformation to a “canonical” basis, in which the structure becomes obvious. Thus, decomposable Lie algebras are already decomposed into direct sums of indecomposable ones. An indecomposable Lie algebra that is not simple or solvable has its radical exhibited. A solvable algebra has its nilradical displayed. The methods all lead to simple algorithms that have been implemented as computer programs, involving some symbolic manipulations.

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