Derivations of First Type of Algebra of Second Class Filiform Leibniz Algebras of Dimension Derivation (n+2)
Pure and Applied Mathematics Journal
Volume 5, Issue 1, February 2016, Pages: 23-31
Received: Dec. 23, 2015; Accepted: Jan. 26, 2016; Published: Feb. 17, 2016
Views 3039      Downloads 86
Author
AL-Nashri AL-Hossain Ahmad, Department of Mathematics, AL Qunfudha University College, Umm AL Qura University, Makkah, Saudia Arabia
Article Tools
Follow on us
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.
Keywords
Filiform Leibniz Algebra, Leibniz Algebra, Gradation, Natural Gradation, Derivation
To cite this article
AL-Nashri AL-Hossain Ahmad, Derivations of First Type of Algebra of Second Class Filiform Leibniz Algebras of Dimension Derivation (n+2), Pure and Applied Mathematics Journal. Vol. 5, No. 1, 2016, pp. 23-31. doi: 10.11648/j.pamj.20160501.14
Copyright
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.
ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186