For Lie algebra $so(2n+1, \mathbb{C})$. There is a matrix representation given by the following matrices:
\begin{align}
\left( \begin{matrix} 0 & x & y \\ -y^T & A & B \\ -x^T & C & -A^T \end{matrix} \right),
\end{align}
where $x, y$ are $1 \times n$ matrices, $A,B,C$ are $n \times n$ matrices. Are there similar matrix representations for Lie group $SO(2n+1, \mathbb{C})$? Thank you very much.