  We study in this paper the infinite-dimensional orthogonal Lie algebra
$\mathcal{O}_C$ which consists of all bounded linear operators $T$ on a
separable, infinite-dimensional, complex Hilbert space $\mathcal{H}$ satisfying
$CTC=-T^*$, where $C$ is a conjugation on $\mathcal{H}$. By employing results
from the theory of complex symmetric operators and skew-symmetric operators, we
determine the Lie ideals of $\mathcal{O}_C$ and their dual spaces. We study
derivations of $\mathcal{O}_C$ and determine their spectra. These results
complete some results of P. de la Harpe and provide interesting contrasts
between $\mathcal{O}_C$ and the algebra $\mathcal{B(H)}$ of all bounded linear
operators on $\mathcal{H}$.
