| Peer-Reviewed

Derivations of First Type of Algebra of Second Class Filiform Leibniz Algebras of Dimension Derivation (n+2)

Received: 23 December 2015     Accepted: 26 January 2016     Published: 17 February 2016
Views:       Downloads:
Abstract

This paper describes the derivations of first type of algebra from the second class filiform Leibniz algebras of dimension derivation (n+2). The set of all derivations of an algebra L is denoted by Der (L) From the description of the derivations, we found the basis of the space Der (Ln (a)) of the algebra.

Published in Pure and Applied Mathematics Journal (Volume 5, Issue 1)
DOI 10.11648/j.pamj.20160501.14
Page(s) 23-31
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Filiform Leibniz Algebra, Leibniz Algebra, Gradation, Natural Gradation, Derivation

References
[1] Albeverio, S., Omirov, B. A., Rakhimov, I. S., (2006), Classification of 4-dimensional nilpotent complex Leibniz algebras, Extracta Math., 3(2006), 197-210.
[2] Dixmier. J. and Lister. W. G., Derivations of nilpotent Lie algebras, Proc. Amer. Math. Soc. 8(1957), 155-158.
[3] M. Goze AND Khakimdjanov, Nilpotent Lie algebras, printed in the netherlands, (1996), 336 p.
[4] Jacobson. N., A note on automorphisms and derivations of Lie algebras, Proc. Amer. Math. Soc. 6(1955), 281–283.
[5] Loday. J. -L., Une version non commutative dés algébras de Lie: les algébras de Leibniz, L’Ens. Math., 39 (1993), 269-293.
[6] Omirov. B. A., On the Derivations of Filiform Leibniz Algebras, Mathematical Notes, 5(2005), 677-685.
[7] Albeverio, S.; Ayupov, Sh. A.; Omirov, B. A., On nilpotent and simple Leibniz algebras, Comm. in Algebra 33(2005), 159-172.
[8] Ayupov, Sh. A.; Omirov, B. A., On Leibniz algebra, Algebra and Operator Theory. Proceeding of the Colloquium in Tashkent (1997), Kluwer (1998), 1-13.
[9] Ayupov, Sh. A.; Omirov, B. A., On 3-dimensional Leibniz algebra, Uzbek Math. (1999), 9–14.
[10] AL-hossain, A. A.; Khiyar, A. A., Derivations of some Filiform Leibniz algebras. pure and Applied mathematics Journal. Vol.3, No. 6, (2014), 121-125.
[11] Alnashri. A. A., Derivations of Second type of algebra of first class Filiform Leibniz algebras of Dimension Derivation (n+1), International Journal of Advanced Scientific and Technical Research, Vol. 3, No. 5, (2015), 29-43.
[12] Alnashri. A. A., Derivations of one type of algebra of First class Filiform Leibniz algebras of Dimension Derivation (n+1), International Journal of Advanced Scientific and Technical Research, Vol. 1, No. 5, (2015), 41-55.
Cite This Article
  • APA Style

    AL-Nashri AL-Hossain Ahmad. (2016). Derivations of First Type of Algebra of Second Class Filiform Leibniz Algebras of Dimension Derivation (n+2). Pure and Applied Mathematics Journal, 5(1), 23-31. https://doi.org/10.11648/j.pamj.20160501.14

    Copy | Download

    ACS Style

    AL-Nashri AL-Hossain Ahmad. Derivations of First Type of Algebra of Second Class Filiform Leibniz Algebras of Dimension Derivation (n+2). Pure Appl. Math. J. 2016, 5(1), 23-31. doi: 10.11648/j.pamj.20160501.14

    Copy | Download

    AMA Style

    AL-Nashri AL-Hossain Ahmad. Derivations of First Type of Algebra of Second Class Filiform Leibniz Algebras of Dimension Derivation (n+2). Pure Appl Math J. 2016;5(1):23-31. doi: 10.11648/j.pamj.20160501.14

    Copy | Download

  • @article{10.11648/j.pamj.20160501.14,
      author = {AL-Nashri AL-Hossain Ahmad},
      title = {Derivations of First Type of Algebra of Second Class Filiform Leibniz Algebras of Dimension Derivation (n+2)},
      journal = {Pure and Applied Mathematics Journal},
      volume = {5},
      number = {1},
      pages = {23-31},
      doi = {10.11648/j.pamj.20160501.14},
      url = {https://doi.org/10.11648/j.pamj.20160501.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20160501.14},
      abstract = {This paper describes the derivations of first type of algebra from the second class filiform Leibniz algebras of dimension derivation (n+2). The set of all derivations of an algebra L is denoted by Der (L) From the description of the derivations, we found the basis of the space Der (Ln (a)) of the algebra.},
     year = {2016}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Derivations of First Type of Algebra of Second Class Filiform Leibniz Algebras of Dimension Derivation (n+2)
    AU  - AL-Nashri AL-Hossain Ahmad
    Y1  - 2016/02/17
    PY  - 2016
    N1  - https://doi.org/10.11648/j.pamj.20160501.14
    DO  - 10.11648/j.pamj.20160501.14
    T2  - Pure and Applied Mathematics Journal
    JF  - Pure and Applied Mathematics Journal
    JO  - Pure and Applied Mathematics Journal
    SP  - 23
    EP  - 31
    PB  - Science Publishing Group
    SN  - 2326-9812
    UR  - https://doi.org/10.11648/j.pamj.20160501.14
    AB  - This paper describes the derivations of first type of algebra from the second class filiform Leibniz algebras of dimension derivation (n+2). The set of all derivations of an algebra L is denoted by Der (L) From the description of the derivations, we found the basis of the space Der (Ln (a)) of the algebra.
    VL  - 5
    IS  - 1
    ER  - 

    Copy | Download

Author Information
  • Department of Mathematics, AL Qunfudha University College, Umm AL Qura University, Makkah, Saudia Arabia

  • Sections