I am learning about Lie algebras and I do not understand the following subalgebra of $\mathfrak gl_{V}$. Let $V$ be a vector space and $\mathfrak gl_{V}$ be the Lie algebra of endomorphisms on $V$. Let $B$ be a bilinear form on a vector space V. Define
$o_{V,B}=\{ a\in \mathfrak{gl}_{V}| B(a(u),v)=-B(u,a(v))~~~ \forall u,v\in V \}$
Im not exactly sure how to ask this question, but I just do not understand this subalgebra. I would like to have some intuition, possibly with an example. Thanks