AIMS Mathematics

2022, Issue 2: 2084-2101. doi: 10.3934/math.2022119
Research article Special Issues

Varieties of a class of elementary subalgebras

• Received: 21 March 2021 Accepted: 13 October 2021 Published: 08 November 2021
• MSC : 17B50

• Let $G$ be a connected standard simple algebraic group of type $C$ or $D$ over an algebraically closed field $\Bbbk$ of positive characteristic $p > 0$, and $\mathfrak{g}: = \mathrm{Lie}(G)$ be the Lie algebra of $G$. Motivated by the variety of $\mathbb{E}(r, \mathfrak{g})$ of $r$-dimensional elementary subalgebras of a restricted Lie algebra $\mathfrak{g}$, in this paper we characterize the irreducible components of $\mathbb{E}(\mathrm{rk}_{p}(\mathfrak{g})-1, \mathfrak{g})$ where the $p$-rank $\mathrm{rk}_{p}(\mathfrak{g})$ is defined to be the maximal dimension of an elementary subalgebra of $\mathfrak{g}$.

Citation: Yang Pan, Yanyong Hong. Varieties of a class of elementary subalgebras[J]. AIMS Mathematics, 2022, 7(2): 2084-2101. doi: 10.3934/math.2022119

Related Papers:

• Let $G$ be a connected standard simple algebraic group of type $C$ or $D$ over an algebraically closed field $\Bbbk$ of positive characteristic $p > 0$, and $\mathfrak{g}: = \mathrm{Lie}(G)$ be the Lie algebra of $G$. Motivated by the variety of $\mathbb{E}(r, \mathfrak{g})$ of $r$-dimensional elementary subalgebras of a restricted Lie algebra $\mathfrak{g}$, in this paper we characterize the irreducible components of $\mathbb{E}(\mathrm{rk}_{p}(\mathfrak{g})-1, \mathfrak{g})$ where the $p$-rank $\mathrm{rk}_{p}(\mathfrak{g})$ is defined to be the maximal dimension of an elementary subalgebra of $\mathfrak{g}$.

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