A simple Lie algebra is a non-abelian Lie algebra that does not have any non-trivial ideals, meaning it cannot be decomposed into smaller, simpler algebras. These algebras are crucial for understanding the structure of Lie groups and their representations, as they are often the building blocks for more complex structures. In the study of symmetries in mathematics and physics, simple Lie algebras play a fundamental role in characterizing the behavior of systems and their underlying symmetries.
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