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

AL-Nashri AL-Hossain Ahmad

doi:doi:10.11648/j.pamj.20160501.14

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

AL-Nashri AL-Hossain Ahmad

Published in Pure and Applied Mathematics Journal (Volume 5, Issue 1)

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

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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 (L_n (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.

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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

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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

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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

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  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},
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  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.},
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Author Information

AL-Nashri AL-Hossain Ahmad

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

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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

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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

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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

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@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