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 ?



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


