Deriving commutator of operators in Lorentz algebra

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The discussion focuses on deriving the commutator of operators in the Lorentz algebra, specifically how to obtain the relation [Li, Lj] = i∈ijkLk from the given expression [Li, Lj] = i/4*∈iab∈jcd(gbcJad - gacJbd - gbdJac + gadJbc). Participants are exploring the implications of the Lorentz commutation relations and the role of the Levi-Civita symbol in the derivation. The original poster seeks clarification on whether the provided expression aids in achieving the desired commutation relation. The conversation emphasizes the mathematical intricacies involved in manipulating these operator relations within the context of theoretical physics. Understanding these derivations is crucial for advancing knowledge in Lorentz algebra applications.
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Homework Statement
How to derive the commutator of L and K according to the Lorentz commutation relations.
Relevant Equations
see below
Li=1/2*∈ijkJjk, Ki=J0i,where J satisfy the Lorentz commutation relation.
[Li,Lj]=i/4*∈iab∈jcd(gbcJad-gacJbd-gbdJac+gadJbc)
How can I obtain
[Li,Lj]=i∈ijkLk
from it?
 
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http://www.physics.mcgill.ca/~guymoore/ph551/appendixC.pdf
 
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