Local superderivations on Lie superalgebra $𝔮\left(n\right)$

Chen, Haixian, and Wang, Ying. "Local superderivations on Lie superalgebra $\mathfrak {q}(n)$." Czechoslovak Mathematical Journal 68.3 (2018): 661-675. <http://eudml.org/doc/294320>.

@article{Chen2018,
abstract = {Let $\mathfrak \{q\}(n)$ be a simple strange Lie superalgebra over the complex field $\mathbb \{C\}$. In a paper by A. Ayupov, K. Kudaybergenov (2016), the authors studied the local derivations on semi-simple Lie algebras over $\mathbb \{C\}$ and showed the difference between the properties of local derivations on semi-simple and nilpotent Lie algebras. We know that Lie superalgebras are a generalization of Lie algebras and the properties of some Lie superalgebras are similar to those of semi-simple Lie algebras, but $\mathfrak \{p\}(n)$ is an exception. In this paper, we introduce the definition of the local superderivation on $\mathfrak \{q\}(n)$, give the structures and properties of the local superderivations of $\mathfrak \{q\}(n)$, and prove that every local superderivation on $\mathfrak \{q\}(n)$, $n>3$, is a superderivation.},
author = {Chen, Haixian, Wang, Ying},
journal = {Czechoslovak Mathematical Journal},
keywords = {simple Lie superalgebra; superderivation; local superderivation},
language = {eng},
number = {3},
pages = {661-675},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Local superderivations on Lie superalgebra $\mathfrak \{q\}(n)$},
url = {http://eudml.org/doc/294320},
volume = {68},
year = {2018},
}

TY - JOUR
AU - Chen, Haixian
AU - Wang, Ying
TI - Local superderivations on Lie superalgebra $\mathfrak {q}(n)$
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 3
SP - 661
EP - 675
AB - Let $\mathfrak {q}(n)$ be a simple strange Lie superalgebra over the complex field $\mathbb {C}$. In a paper by A. Ayupov, K. Kudaybergenov (2016), the authors studied the local derivations on semi-simple Lie algebras over $\mathbb {C}$ and showed the difference between the properties of local derivations on semi-simple and nilpotent Lie algebras. We know that Lie superalgebras are a generalization of Lie algebras and the properties of some Lie superalgebras are similar to those of semi-simple Lie algebras, but $\mathfrak {p}(n)$ is an exception. In this paper, we introduce the definition of the local superderivation on $\mathfrak {q}(n)$, give the structures and properties of the local superderivations of $\mathfrak {q}(n)$, and prove that every local superderivation on $\mathfrak {q}(n)$, $n>3$, is a superderivation.
LA - eng
KW - simple Lie superalgebra; superderivation; local superderivation
UR - http://eudml.org/doc/294320
ER -