Solvable Lie algebras with nilradicals of orthogonal types (Q2905186)

Let \(n\) \((\geq 4)\) be a positive integer, \(\mathfrak n\) a standard maximal nilpotent subalgebra of the orthogonal algebra \(\mathfrak o(2n, F)\) over a field \(F\) of characteristic not \(2\) and \(\mathfrak s\) a solvable Lie algebra containing \(\mathfrak n\) as its nilradical. The authors determine all derivations of \(\mathfrak n\), introduce an automorphism of \(\mathfrak n\), and show that the dimension of \(\mathfrak s\) is at most \(\dim(\mathfrak n)+n\). Moreover, \(\mathfrak s\) is isomorphic to the standard Borel subalgebra \(\mathfrak b\) of \(\mathfrak o(2n, F )\) if and only if \(\dim(\mathfrak s) = \dim(\mathfrak n)+n\).