Journal of Lie Theory

no. 3
Solvable Lie Algebras with Nilradicals of Orthogonal Types
Dengyin Wang1; Hongya Bian1; Bingkai Chen1
1School of Science, China University of Mining and Technology, Xuzhou 221008, P. R. China
Journal of Lie Theory, Volume 22 (2012) no. 3, pp. 683-699
\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 $\dim(\s)=\dim(\n)+n$.
DOI: 10.5802/jolt.686
Classification: 17B05, 17B20, 17B30, 17B40
Keywords: Solvable Lie algebras, derivations, nilradicals

Dengyin Wang  1 ; Hongya Bian  1 ; Bingkai Chen  1

1 School of Science, China University of Mining and Technology, Xuzhou 221008, P. R. China 
Dengyin Wang; Hongya Bian; Bingkai Chen. Solvable Lie Algebras with Nilradicals of Orthogonal Types. Journal of Lie Theory, Volume 22 (2012) no. 3, pp. 683-699. doi: 10.5802/jolt.686
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     author = {Dengyin Wang and Hongya Bian and Bingkai Chen},
     title = {Solvable {Lie} {Algebras} with {Nilradicals} of {Orthogonal} {Types}},
     journal = {Journal of Lie Theory},
     pages = {683--699},
     year = {2012},
     volume = {22},
     number = {3},
     doi = {10.5802/jolt.686},
     zbl = {1257.17016},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.686/}
}
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