Journal of Lie Theory 22 (2012), No. 3, 683--699
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
[Abstract-pdf]
\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
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