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Czechoslovak Mathematical Journal

, Volume 68, Issue 3, pp 661–675 | Cite as

Local Superderivations on Lie Superalgebra \(\mathfrak{q}\) (n)

  • Haixian Chen
  • Ying Wang
Article

Abstract

Let \(\mathfrak{q}\) (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 \(\mathfrak{p}\) (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.

Keywords

simple Lie superalgebra superderivation local superderivation 

MSC 2010

16W55 17B20 17B40 

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References

  1. [1]
    S. Albeverio, S. A. Ayupov, K. K. Kudaybergenov, B. O. Nurjanov: Local derivations on algebras of measurable operators. Commun. Contemp. Math. 13 (2011), 643–657.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    R. Alizadeh, M. J. Bitarafan: Local derivations of full matrix rings. Acta Math. Hung. 145 (2015), 433–439.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    S. Ayupov, K. Kudaybergenov: Local derivations on finite-dimensional Lie algebras. Linear Algebra Appl. 493 (2016), 381–398.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    S. Ayupov, K. Kudaybergenov, B. Nurjanov, A. Alauadinov: Local and 2-local derivations on noncommutative Arens algebras. Math. Slovaca 64 (2014), 423–432.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    V. G. Kac: Lie superalgebras. Adv. Math. 26 (1977), 8–96.CrossRefzbMATHGoogle Scholar
  6. [6]
    R. V. Kadison: Local derivations. J. Algebra 130 (1990), 494–509.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    F. Mukhamedov, K. Kudaybergenov: Local derivations on subalgebras of t-measurable operators with respect to semi-finite von Neumann algebras. Mediterr. J. Math. 12 (2015), 1009–1017.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    I. M. Musson: Lie Superalgebras and Enveloping Algebras. Graduate Studies in Mathematics 131, American Mathematical Society, Providence, 2012.Google Scholar
  9. [9]
    A. Nowicki, I. Nowosad: Local derivations of subrings of matrix rings. Acta Math. Hung. 105 (2004), 145–150.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    M. Scheunert: The Theory of Lie Superalgebras. An Introduction. Lecture Notes in Mathematics 716, Springer, Berlin, 1979.Google Scholar
  11. [11]
    J.-H. Zhang, G.-X. Ji, H.-X. Cao: Local derivations of nest subalgebras of von Neumann algebras. Linear Algebra Appl. 392 (2004), 61–69.MathSciNetCrossRefzbMATHGoogle Scholar

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 CityP.R. China

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