
Journal of Lie Theory 22 (2012), No. 3, 683699 Copyright Heldermann Verlag 2012 Solvable Lie Algebras with Nilradicals of Orthogonal Types Dengyin Wang School of Science, China University of Mining and Technology, Xuzhou 221008, P. R. China wdengyin@126.com Hongya Bian School of Science, China University of Mining and Technology, Xuzhou 221008, P. R. China Bingkai Chen School of Science, China University of Mining and Technology, Xuzhou 221008, P. R. China [Abstractpdf] \def\b{{\frak b}} \def\n{{\frak n}} \def\s{{\frak s}} Let $n\geq 4$ be a positive integer, $\n$ a maximal nilpotent subalgebra of the orthogonal algebra o$(2n,F)$ over a field $F$ of characteristic not $2$, $\s$ a solvable Lie algebra containing $\n$ as its nilradical. This article shows that the dimension of $\s$ is at most $\dim(\n)+n$, and $\s$ is isomorphic to the standard Borel subalgebra $\b$ of o$(2n,F)$ if and only if $\dim(\s)=\dim(\n)+n$. Keywords: Solvable Lie algebras, derivations, nilradicals. MSC: 17B05, 17B20, 17B30, 17B40 [ Fulltextpdf (284 KB)] for subscribers only. 