IJPAM: Volume 113, No. 2 (2017)

Title

CENTROIDS AND QUASI-CENTROIDS OF
FINITE DIMENSIONAL LEIBNIZ ALGEBRAS

Authors

Hassan Almutari$^1$, Abd Ghafur Ahmad$^2$
$^{1,2}$School of Mathematics
Faculty of Science and Technology
Universiti Kebangsaan Malaysia
43600, Selangor Darul-Ehsan, MALAYSIA

Abstract

We introduce the concept of centroid and quasicentroids for Leibniz algebras and study some of their properties. Then we determine the centroids of low-dimensional Leibniz algebras and give their classification.

History

Received: August 27, 2016
Revised: January 1, 2017
Published: March 19, 2017

AMS Classification, Key Words

AMS Subject Classification: 16D70
Key Words and Phrases: Leibniz algebra, centroid, quasicentroids, derivation, central derivation

Download Section

Download paper from here.
You will need Adobe Acrobat reader. For more information and free download of the reader, see the Adobe Acrobat website.

Bibliography

1
Albeverio, S., Omirov, B. and Rakhimov, I., Classification of 4-dimensional nilpotent complex Leibniz algebras, Extracta Math ., 3(1), (2006), 197-210.

2
G. Benkart, E. Neher, The centroid of extended affine and root graded Lie algebras, Journal of Pure and Applied Algebra, 205(1), (2006), 117-145.

3
Casas, J., Insua, M., M. and Ladra, S., An algorithm for the classification of $3$-dimensional complex Leibniz algebras, Linear Algebra and Its Applications., 40(8), (2012), 2962-2982.

4
Loday J.-L.,Une version non commutative désde Lie: les de Leibniz. L'Ens. Math., Publ. Math. I.H.E.S., 39, (1993), 269-293.

5
Loday J.-L., Frabetti A., Chapoton F., Goichot F. Dialgebras and Related Operads, Lecture Notes in Math., 1763, Springer, Berlin, (2001).

6
D.J. Melville, Centroids of nilpotent Lie algebras, Comm. Algebra, 20(12), (1992), 3649-3682.

7
Melville D.J., Centroids and Cartan algebras, Comm. Algebra, 21(8), (1993),2791-2818.

How to Cite?

DOI: 10.12732/ijpam.v113i2.2 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 113
Issue: 2
Pages: 203 - 217


Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).