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Every non-solvable and non-semisimple quadratic Lie algebra can be obtainedas a double extension of a solvable quadratic Lie algebra. Thanks to a partialclassification of nilpotent Lie algebras and this result, we can designdifferent techniques to obtain any quadratic Lie algebra whose (solvable)radical ideal is nilpotent. To achieve this, we propose two alternativemethods, both involving the use of quotients. In addition to their mathematicaldescription, both approaches introduced in this paper have been computationallyimplemented and are publicly available to use for generating these algebras.

Computing Derivations on Nilpotent Quadratic Lie Algebras