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Reductive Lie algebra

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Representation Theory of Lie Groups Ias Park City Mathematics Series, V 8

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Derived algebraic geometry and deformation quantization

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Donna Testerman, lauréate du Credit Suisse Award for best teaching 2020

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[Wikipedia] Theory of Lie groups

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In mathematics, a Lie algebra is reductive if its adjoint representation is completely reducible, whence the name. More concretely, a Lie algebra is reductive if it is a direct sum of a semisimple Lie algebra and an abelian Lie algebra: there are alternative characterizations, given below.
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