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An anyonic Lie algebra is a mathematical structure that arises in the study of anyons, which are quasiparticles that exist in two-dimensional systems. Anyons are characterized by their statistics, which can be neither fermionic (obeying the Pauli exclusion principle) nor bosonic (which obey Bose-Einstein statistics). Instead, anyons can acquire a phase that is neither 0 nor π when two of them are exchanged, making their statistical behavior more complex and rich.

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