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2-Nilpotent multipliers of a direct product of Lie algebras

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Abstract

In this paper, we present an explicit formula for the 2-nilpotent multiplier of a direct product of two Lie algebras.

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References

  1. Batten, P.: Multipliers and covers of Lie algebras, Dissertation. State University, North Carolina (1993)

    Google Scholar 

  2. Batten, P., Moneyhun, K., Stitzinger, E.: On characterizing nilpotent Lie algebras by their multipliers. Commun. Algebra 24, 4319–4330 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  3. Batten, P., Stitzinger, E.: On covers of Lie algebras. Commun. Algebra 24, 4301–4317 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bosko, L.: On Schur Multipliers of Lie algebras and groups of maximal class. Internat. J. Algebra Comput. 20, 807–821 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  5. Burns, J., Ellis, G.: On the nilpotent multipliers of a group. Math. Z. 226, 405–428 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  6. Hardy, P.: On characterizing nilpotent Lie algebras by their multipliers III. Comm. Algebra 33, 4205–4210 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  7. Hardy, P., Stitzinger, E.: On characterizing nilpotent Lie algebras by their multiplierst \(t(L) = 3,4,5,6\). Commun. Algebra 26, 3527–3539 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  8. Mashayekhy, B., Sanati, M.A.: On the order of nilpotent multipliers of finite \(p\)-groups. Commun. Algebra 33(7), 2079–2087 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  9. Niroomand, P.: On dimension of the Schur multiplier of nilpotent Lie algebras. Cent. Eur. J. Math. 9, 57–64 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. Niroomand, P., Parvizi, M.: On the 2-nilpotent multiplier of finite \(p\)-groups. Glasg. Math. J. 57(1), 201–210 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  11. Niroomand, P., Russo, F.G.: A note on the Schur multiplier of a nilpotent Lie algebra. Commun. Algebra 39, 1293–1297 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  12. Niroomand, P., Russo, F.G.: A restriction on the Schur multiplier of nilpotent Lie algebras. Electron. J. Linear Algebra 22, 1–9 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  13. Salemkar, A.R., Mirzaei, F.: Characterizing n-isoclinism classes of Lie algebras. Commun. Algebra 38, 3392–3403 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  14. Salemkar, A.R., Bigdely, H., Alamian, V.: Some properties on isoclinism of Lie algebras and covers. J. Algebra Appl. 7, 507–516 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  15. Salemkar, A.R., Alamian, V., Mohammadzadeh, H.: Some properties of the Schur multiplier and covers of Lie algebras. Commun. Algebra 36, 697–707 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  16. Shirshov, A.I.: On bases of free Lie algebras. Algebra Log. 1(1), 14–19 (1962)

    MathSciNet  MATH  Google Scholar 

  17. Shirshov, A.I.: Selected Works of A. I. Shirshov. Translated from the Russian by Bremner, M., Kotchetov, M.V. In: Bokut, L.A., Latyshev, V., Shestakov, I., Zelmanov, E. (eds.) Contemporary Mathematicians, pp viii+242. ISBN 978-3-7643-8857-7. Birkhäuser Verlag, Basel (2009)

  18. Tappe, J.: On isoclinic groups. Math. Z. 148, 147–153 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  19. Yankoski, B.: On the multiplier of a Lie Algebra. J. Lie Theory 13, 1–6 (2003)

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Damghan University, Damghan, Iran

    Peyman Niroomand

  2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran

    Peyman Niroomand

  3. Department of Pure Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

    Mohsen Parvizi

Authors
  1. Peyman Niroomand
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  2. Mohsen Parvizi
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Corresponding author

Correspondence to Peyman Niroomand.

Additional information

The first authors research was in part supported by a grant from IPM (No. 94160063).

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Niroomand, P., Parvizi, M. 2-Nilpotent multipliers of a direct product of Lie algebras. Rend. Circ. Mat. Palermo, II. Ser 65, 519–523 (2016). https://doi.org/10.1007/s12215-016-0251-0

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  • DOI: https://doi.org/10.1007/s12215-016-0251-0

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