Decomposition of automorphisms of certain solvable subalgebra of symplectic Lie algebra over commutative rings (Q715115)

Summary: Let \(C_{l+1}(R)\) be the \(2(l + 1) \times 2(l + 1)\) matrix symplectic Lie algebra over a commutative ring \(R\) with 2 invertible. Then \textbf{t}\(^{(C)}_{l+1}(R) = \Biggl\{\left( \begin{matrix} \overline{m}_1 & \overline{m}_2\\ 0 & -\overline{m}^{T}_1 \end{matrix} \right)\mid \overline{m}_1\) is an \(l + 1\) upper triangular matrix, \(\overline{m}^T_2 = \overline{m}_2\), over \(R\) is the solvable subalgebra of \(C_{l+1}(R)\bigr\}\). In this paper, we give an explicit description of the automorphism group of \textbf{t}\(^{(C)}_{l+1}(R)\).