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.
simple Lie superalgebra superderivation local superderivation
16W55 17B20 17B40
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F. Mukhamedov, K. Kudaybergenov: Local derivations on subalgebras of τ-measurable operators with respect to semi-finite von Neumann algebras. Mediterr. J. Math. 12 (2015), 1009–1017MathSciNetCrossRefMATHGoogle Scholar
I. M. Musson: Lie Superalgebras and Enveloping Algebras. Graduate Studies in Mathematics 131, American Mathematical Society, Providence, 2012.MATHGoogle Scholar