A Lie algebra is a mathematical structure that studies the properties of continuous transformation groups, specifically those associated with Lie groups. It consists of a vector space equipped with a binary operation known as the Lie bracket, which satisfies bilinearity, alternativity, and the Jacobi identity. This concept plays a crucial role in understanding symmetries and their algebraic properties, particularly in the study of isometry groups and the broader framework of Lie groups and their algebras.
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