# Local superderivations on Lie superalgebra $\U0001d52e\left(n\right)$

Czechoslovak Mathematical Journal (2018)

- Volume: 68, Issue: 3, page 661-675
- ISSN: 0011-4642

## Access Full Article

top## Abstract

top## How to cite

topChen, 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 -

## References

top- Albeverio, S., Ayupov, S. A., Kudaybergenov, K. K., Nurjanov, B. O., 10.1142/S0219199711004270, Commun. Contemp. Math. 13 (2011), 643-657. (2011) Zbl1230.46056MR2826440DOI10.1142/S0219199711004270
- Alizadeh, R., Bitarafan, M. J., 10.1007/s10474-014-0460-y, Acta Math. Hung. 145 (2015), 433-439. (2015) Zbl1363.17003MR3325800DOI10.1007/s10474-014-0460-y
- Ayupov, S., Kudaybergenov, K., 10.1016/j.laa.2015.11.034, Linear Algebra Appl. 493 (2016), 381-398. (2016) Zbl06536636MR3452744DOI10.1016/j.laa.2015.11.034
- Ayupov, S., Kudaybergenov, K., Nurjanov, B., Alauadinov, A., 10.2478/s12175-014-0215-9, Math. Slovaca 64 (2014), 423-432. (2014) Zbl1349.46071MR3201356DOI10.2478/s12175-014-0215-9
- Kac, V. G., 10.1016/0001-8708(77)90017-2, Adv. Math. 26 (1977), 8-96. (1977) Zbl0366.17012MR0486011DOI10.1016/0001-8708(77)90017-2
- Kadison, R. V., 10.1016/0021-8693(90)90095-6, J. Algebra 130 (1990), 494-509. (1990) Zbl0751.46041MR1051316DOI10.1016/0021-8693(90)90095-6
- Mukhamedov, F., Kudaybergenov, K., 10.1007/s00009-014-0447-5, Mediterr. J. Math. 12 (2015), 1009-1017. (2015) Zbl1321.47089MR3376827DOI10.1007/s00009-014-0447-5
- Musson, I. M., 10.1090/gsm/131, Graduate Studies in Mathematics 131, American Mathematical Society, Providence (2012). (2012) Zbl1255.17001MR2906817DOI10.1090/gsm/131
- Nowicki, A., Nowosad, I., 10.1023/B:AMHU.0000045539.32024.db, Acta Math. Hung. 105 (2004), 145-150. (2004) Zbl1070.16035MR2093937DOI10.1023/B:AMHU.0000045539.32024.db
- Scheunert, M., 10.1007/bfb0070929, Lecture Notes in Mathematics 716, Springer, Berlin (1979). (1979) Zbl0407.17001MR0537441DOI10.1007/bfb0070929
- Zhang, J.-H., Ji, G.-X., Cao, H.-X., 10.1016/j.laa.2004.05.015, Linear Algebra Appl. 392 (2004), 61-69. (2004) Zbl1067.46063MR2095907DOI10.1016/j.laa.2004.05.015

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.