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Lie derivations of certain CSL algebras

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Abstract

It is shown that each Lie derivation on a reflexive algebra, whose lattice is completely distributive and commutative, can be uniquely decomposed into the sum of a derivation and a linear mapping with image in the center of the algebra.

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References

  1. J. Alaminos, M. Mathieu and A. R. Villena,Symmetric amenability and Lie derivations, Mathematical Proceedings of the Cambridge Philosophical Society137 (2004), 433–439.

    Article  MATH  MathSciNet  Google Scholar 

  2. W. Arveson,Operator algebra and invariant subspace, Annals of Mathematics100 (1974), 433–532.

    Article  MathSciNet  Google Scholar 

  3. K. I. Beidar and M. A. Chebotar,On lie derivations of Lie ideals of prime rings, Israel Journal of Mathematics123 (2001), 131–148.

    MATH  MathSciNet  Google Scholar 

  4. M. Brešar,Commuting traces of biadditive mappings, commutativity-preserving mappings and Lie mappings, Transactions of the American Mathematical Society335 (1993), 525–546.

    Article  MathSciNet  MATH  Google Scholar 

  5. W. Cheung,Lie derivations of triangular algebras, Linear and Multilinear Algebra51 (2003), 299–310.

    Article  MATH  MathSciNet  Google Scholar 

  6. E. Christensen,Derivations of nest algebras, Mathematische Annalen229 (1977), 155–161.

    Article  MATH  MathSciNet  Google Scholar 

  7. Gilfeather and R. L. Moore,Isomorphisms of certain CSL algebras, Journal of Functional Analysis67 (1986), 264–291.

    Article  MATH  MathSciNet  Google Scholar 

  8. D. Hadwin and J. Li,Local derivations and local automorphisms, Journal of Mathematical Analysis and Applications290 (2004), 702–714

    Article  MATH  MathSciNet  Google Scholar 

  9. P. R. Halmos,A Hilbert Space Problem Book, 2nd edn., Springer-Verlag, New York/Heideberg/Berlin, 1982.

    MATH  Google Scholar 

  10. A. Hopenwasser,Complete distributivity, Proceedings of Symposia in Pure Mathematics51 (1990), 285–305.

    MathSciNet  Google Scholar 

  11. B. E. Johnson,Symmetric amenability and the nonexistence of Lie and Jordan derivations, Mathematical Proceedings of the Cambridge Philosophical Society120 (1996), 455–473.

    Article  MATH  MathSciNet  Google Scholar 

  12. M. S. Lambrou,Completely distributive lattices, Fundamenta Mathematica119 (1983), 227–240.

    MATH  MathSciNet  Google Scholar 

  13. C. Laurie and W. E. Longstaff,A note on rank one operators in reflexive algebras, Proceedings of the American Mathematical Society89 (1983), 293–297.

    Article  MathSciNet  Google Scholar 

  14. W. E. Logstaff,Strongly reflexive lattices, Journal of the London Mathematical Society11 (1975), 491–498.

    Article  Google Scholar 

  15. W. E. Longstaff,Operators of rank one in reflexive algebras, Canadian Journal of Mathematics28 (1976), 9–23.

    Google Scholar 

  16. F. Lu,Jordan structure of CSL algebras, Manuscript.

  17. W. S. Martindale,Lie derivations of Primitive rings, Michigan Mathematical Journal11 (1964), 183–187.

    Article  MATH  MathSciNet  Google Scholar 

  18. M. Mathieu and A. R. Villena,The structure of Lie derivations on C *-algebras, Journal of Functional Analysis202 (2003), 504–525.

    Article  MATH  MathSciNet  Google Scholar 

  19. C. R. Miers,Lie derivations of von Neumann algebras, Duke Mathematical Journal40 (1973), 403–409.

    Article  MATH  MathSciNet  Google Scholar 

  20. G. A. Swain,Lie derivations of the skew elements of prime rings with involution, Journal of Algebra184 (1996), 679–704.

    Article  MATH  MathSciNet  Google Scholar 

  21. G. A. Swain and P. S. Blau,Lie derivations in prime rings with involution, Canadian Mathematical Bulletin42 (1999), 401–411.

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Suzhou University, 215006, Suzhou, P. R. China

    Fangyan Lu

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  1. Fangyan Lu
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Additional information

Supported by NNSFC (No. 10571054) and a grant (No.04KJB110116) from the government of Jiangsu Province of China.

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Lu, F. Lie derivations of certain CSL algebras. Isr. J. Math. 155, 149–156 (2006). https://doi.org/10.1007/BF02773953

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  • DOI: https://doi.org/10.1007/BF02773953

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