| Summary: | In this paper, we propose the representation and cohomology of modified <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula>-differential 3-Lie algebras. As their applications, the linear deformations, abelian extensions and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>T</mi><mo>∗</mo></msup></semantics></math></inline-formula>-extensions of modified <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula>-differential 3-Lie algebras are also studied.
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