Theory of Extensions of Multiplicative Lie Algebras

Key Points

• The study aims to define second cohomology for multiplicative Lie algebras and explore their extensions.
• Defined second cohomology of a multiplicative Lie algebra with coefficients in an abelian group
• Established a bijective correspondence between second cohomology and equivalence classes of extensions
• Introduced the concept of Baer sum for extensions in this algebraic context.
• Demonstrated a natural bijective correspondence between second cohomology and equivalence classes of specific extensions
• Outlined the framework for defining Baer sums of extensions in multiplicative Lie algebras.