\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 $\g$.
1
School of Sciences, Zhejiang A&F University, Huanbei Road 88, 311300 Hangzhou, P.R.China
2
Mathematisches Seminar, Universität Kiel, Ludewig-Meyn-Str. 4, 24098 Kiel, Germany
Yang Pan. Varieties of Elementary Subalgebras of Submaximal Rank in Type A. Journal of Lie Theory, Tome 28 (2018) no. 1, pp. 57-70. http://geodesic.mathdoc.fr/item/JOLT_2018_28_1_a3/
@article{JOLT_2018_28_1_a3,
author = {Yang 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},
url = {http://geodesic.mathdoc.fr/item/JOLT_2018_28_1_a3/}
}
TY - JOUR
AU - Yang Pan
TI - Varieties of Elementary Subalgebras of Submaximal Rank in Type A
JO - Journal of Lie Theory
PY - 2018
SP - 57
EP - 70
VL - 28
IS - 1
UR - http://geodesic.mathdoc.fr/item/JOLT_2018_28_1_a3/
ID - JOLT_2018_28_1_a3
ER -
%0 Journal Article
%A Yang 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 http://geodesic.mathdoc.fr/item/JOLT_2018_28_1_a3/
%F JOLT_2018_28_1_a3
