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