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How i can write general relativity Lorentz connection ( $A^{a} _ {\ \ bc}$ ) in term of structure coefficients ( $f^a_{\ \ bc}$ ) ? $\ \ $ I know the relation:

$A^a_{\ \ bc}$=$1/2$( $f^{\ a} _ {b\ c}$ +$f^{\ a} _ {c\ b}$ -$f^{a}_{\ \ bc} )$

But i couldn't derive it ! Any References ?

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Use the Koszul formula in a orthonormal frame (see O'Neill B. "Semi-Riemannian geometry", AP, 1983, Chapter 3, Theorem 11).

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