Triple automorphisms of simple Lie algebras
Czechoslovak Mathematical Journal (2011)
- Volume: 61, Issue: 4, page 1007-1016
- ISSN: 0011-4642
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topWang, Deng Yin, and Yu, Xiaoxiang. "Triple automorphisms of simple Lie algebras." Czechoslovak Mathematical Journal 61.4 (2011): 1007-1016. <http://eudml.org/doc/197191>.
@article{Wang2011,
abstract = {An invertible linear map $\varphi $ on a Lie algebra $L$ is called a triple automorphism of it if $\varphi ([x,[y,z]])=[\varphi (x),[ \varphi (y),\varphi (z)]]$ for $\forall x, y, z\in L$. Let $\mathfrak \{g\}$ be a finite-dimensional simple Lie algebra of rank $l$ defined over an algebraically closed field $F$ of characteristic zero, $\mathfrak \{p\}$ an arbitrary parabolic subalgebra of $\mathfrak \{g\}$. It is shown in this paper that an invertible linear map $\varphi $ on $\mathfrak \{p\}$ is a triple automorphism if and only if either $\varphi $ itself is an automorphism of $\mathfrak \{p\}$ or it is the composition of an automorphism of $\mathfrak \{p\}$ and an extremal map of order $2$.},
author = {Wang, Deng Yin, Yu, Xiaoxiang},
journal = {Czechoslovak Mathematical Journal},
keywords = {simple Lie algebras; parabolic subalgebras; triple automorphisms of Lie algebras; simple Lie algebra; parabolic subalgebra; triple automorphisms of Lie algebras},
language = {eng},
number = {4},
pages = {1007-1016},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Triple automorphisms of simple Lie algebras},
url = {http://eudml.org/doc/197191},
volume = {61},
year = {2011},
}
TY - JOUR
AU - Wang, Deng Yin
AU - Yu, Xiaoxiang
TI - Triple automorphisms of simple Lie algebras
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 4
SP - 1007
EP - 1016
AB - An invertible linear map $\varphi $ on a Lie algebra $L$ is called a triple automorphism of it if $\varphi ([x,[y,z]])=[\varphi (x),[ \varphi (y),\varphi (z)]]$ for $\forall x, y, z\in L$. Let $\mathfrak {g}$ be a finite-dimensional simple Lie algebra of rank $l$ defined over an algebraically closed field $F$ of characteristic zero, $\mathfrak {p}$ an arbitrary parabolic subalgebra of $\mathfrak {g}$. It is shown in this paper that an invertible linear map $\varphi $ on $\mathfrak {p}$ is a triple automorphism if and only if either $\varphi $ itself is an automorphism of $\mathfrak {p}$ or it is the composition of an automorphism of $\mathfrak {p}$ and an extremal map of order $2$.
LA - eng
KW - simple Lie algebras; parabolic subalgebras; triple automorphisms of Lie algebras; simple Lie algebra; parabolic subalgebra; triple automorphisms of Lie algebras
UR - http://eudml.org/doc/197191
ER -
References
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