Theory defines cohomology and bijective correspondence for extensions in multiplicative lie algebras, suggesting new frameworks.
We define the second cohomology of a multiplicative Lie algebra K with coefficients in an abelian group H with trivial multiplicative Lie algebra structure in two different cases.Consequently, we prove a natural bijective correspondence between the second cohomology and the set of equivalence classes of some special type of extensions.We also define the notion of Baer sum of extensions for multiplicative Lie algebras.
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Pandey et al. (2021) studied this question.
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