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in this link :http://gallica.bnf.fr/ark:/12148/bpt6k7258/f122.image

The equation 2b is not correct I believe. Please correct me if I'm wrong.

Here we go :

The equation mentioned reads : R^{αβλ}_{μ}R_{αβλρ}= 2 * 1/8 * R^{αβλμ}R_{αβλμ}g_{μρ}

Now multiply out by g^{μρ}on both sides and elevate the μ index on the LHS, we would end up having :

R^{αβλε}g_{με}R_{αβλρ}g^{μρ}=

2 * 1/8 * R^{αβλμ}R_{αβλμ}g_{μρ}g^{μρ}

This becomes :

R^{αβλε}δ_{ε}^{ρ}R_{αβλρ}=

2 * 1/8 * R^{αβλμ}R_{αβλμ}g_{μρ}g^{μρ}

which leads to :

R^{αβλρ}R_{αβλρ}= 2 * 1/8 * R^{αβλμ}R_{αβλμ}g_{μρ}g^{μρ}

On the RHS, do we agree that the indices on the g's are not to be summed over since they are fixed ones ? This means that the product of the g's is 1 (if they were summation indices, we would get 4 and not 1) , which results in :

R^{αβλρ}R_{αβλρ}= 2 * 1/8 * R^{αβλμ}R_{αβλμ}

But THIS IS WRONG ! the μ on the LHS of the equation should not be the same μ as on the RHS since it is a fixed index I believe.

thank you,

Cheers,

PS: I have seen the referenced Lanczos paper but there is no way you can tell how Bel ended up with that one !

PS: Here :http://arxiv.org/pdf/1006.3168v4

in the first paragraph, the author is referring to another variant of the Lanczos formula ! and this is correct I think

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# Error in Bel's 1958 article ? Lanczos formula incorrectly reported

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