Local Superderivations on Lie Superalgebra q(n)

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Abstract

Let q(n) be a simple strange Lie superalgebra over the complex field ℂ. In a paper by A. Ayupov, K. Kudaybergenov (2016), the authors studied the local derivations on semi-simple Lie algebras over 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 p(n) is an exception. In this paper, we introduce the definition of the local superderivation on q(n), give the structures and properties of the local superderivations of q(n), and prove that every local superderivation on q(n), n > 3, is a superderivation.

Keywords

simple Lie superalgebra superderivation local superderivation 

MSC 2010

16W55 17B20 17B40 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesDalian University of TechnologyDalian City, Liaoning ProvinceP. R. China

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