Journal of Lie Theory

no. 1
Varieties of Elementary Subalgebras of Submaximal Rank in Type A
Journal of Lie Theory, Volume 28 (2018) no. 1, pp. 57-70
\def\g{{\frak g}} \def\E{\mathbb E} Let $G$ be a connected simple algebraic group over an algebraically closed field {\bf k} of characteristic $p>0$, and $\g$ = lie$(G)$. We additionally assume that $G$ is standard and is of type $A_{n}$. Motivated by the investigation of the geometric properties of the varieties $\E(r,\g)$ of $r$-dimensional elementary subalgebras of a restricted Lie algebra $\g$, we will show in this article the irreducible components of $\E({\rm rk}_p(\g)-1,\g)$ when rk$_p(\g)$ is the maximal dimension of an elementary subalgebra of $\g$.
DOI: 10.5802/jolt.993
Classification: 17B50, 16G10
Keywords: Elementary subalgebras, irreducible components 
@article{JOLT_2018_28_1_a3,
     author = {Y. Pan},
     title = {Varieties of {Elementary} {Subalgebras} of {Submaximal} {Rank} in {Type} {A}},
     journal = {Journal of Lie Theory},
     pages = {57--70},
     year = {2018},
     volume = {28},
     number = {1},
     doi = {10.5802/jolt.993},
     zbl = {1433.17022},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.993/}
}
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%A Y. Pan
%T Varieties of Elementary Subalgebras of Submaximal Rank in Type A
%J Journal of Lie Theory
%D 2018
%P 57-70
%V 28
%N 1
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.993/
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Y. Pan. Varieties of Elementary Subalgebras of Submaximal Rank in Type A. Journal of Lie Theory, Volume 28 (2018) no. 1, pp. 57-70. doi: 10.5802/jolt.993

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