Factorization in the context of Lie algebras refers to the process of breaking down a given Lie algebra into simpler components, often using ideals and quotient structures. This is significant because it allows for a better understanding of the structure and properties of the Lie algebra by examining these simpler components. The concept is closely tied to ideals, which are specific subalgebras that help facilitate this breakdown, leading to quotient Lie algebras that represent the relationships between the original algebra and its ideals.
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