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gptkb:Lie_algebra_sl(5)
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given by commutator of matrices
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gptkb:su(2)
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gptkb:Levi-Civita_symbol
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gptkb:sp_{2n}(F)_(Lie_algebra)
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depend on symplectic form
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gptkb:gl(n,C)
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matrix commutator
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gptkb:SU(N)_algebra
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f^{abc}
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gptkb:SU(2)_algebra
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gptkb:Levi-Civita_symbol
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gptkb:general_linear_Lie_algebra
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gptkb:Kronecker_delta
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gptkb:sp(2n,_F)
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depend on symplectic form
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gptkb:special_linear_Lie_algebra_over_the_real_numbers
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given by commutator of matrices
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gptkb:A_2_Lie_algebra
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well-defined
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gptkb:Lie_algebra_sl(2,_R)
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[H,E]=2E, [H,F]=-2F, [E,F]=H
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gptkb:sl(n,_C)
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[E_{ij}, E_{kl}] = δ_{jk}E_{il} - δ_{il}E_{kj}
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gptkb:Lie_algebra_so(n+1,_C)
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antisymmetric
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gptkb:sl(2,C)
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[H,E]=2E, [H,F]=-2F, [E,F]=H
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gptkb:sp(2n,_C)
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depends on symplectic form
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gptkb:su(3)
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antisymmetric
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gptkb:unitary_Lie_algebra
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antisymmetric
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gptkb:rotation_algebra_so(3)
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gptkb:Levi-Civita_symbol
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gptkb:sl(n,_R)
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dependent on n
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gptkb:sl(3,R)
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given by commutator of matrices
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