Hi please can someone help me $(A <, >)$ a flat pseudo-euclidien Lie algebra which contains bilateral ideal I and also its orthogonal is bilateral ideal.

I don't understand why: if The restriction of $ <,> $, to $I^{\perp}$ is degenerate have radical=I. So $<,>_{I^{\perp} \times I^{\perp}}$ defined by passing to the quotient a non-degenerate symmetric bilinear form on $B=I^{\perp} / I$