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1. Lie Bracket

   Linked via "infinitesimal transformations"

   The Lie bracket (sometimes denoted as the Poisson bracket (Hamiltonian mechanics)/) when contextually related to Hamiltonian mechanics) is a fundamental operation in the mathematical structures known as Lie algebras and Lie groups. It serves primarily to quantify the failure of associativity or commutativity of the underlying algebraic structure, often interpreted geometrically as the failure of [infinit…