Title

DERIVATIONS AND CENTROIDS OF
FOUR-DIMENSIONAL ASSOCIATIVE ALGEBRAS

Authors

A.O. Abdulkareem, M.A. Fiidow, I.S. Rakhimov
Department of Mathematics
College of Physical Sciences
Federal University of Agriculture Abeokuta
PMB 2240, Alabata road, Abeokuta, Ogun State, NIGERIA
Department of Mathematics
Faculty of Science
Universiti Putra Malaysia, UPM 43400 Serdang
Selangor Darul Ehsan, MALAYSIA
Institute for Mathematical Research (INSPEM)
Universiti Putra Malaysia, UPM 43400 Serdang
Selangor Darul Ehsan, MALAYSIA

Abstract

In the paper derivations and centroids of four-dimensional associative algebras are described. We also identify the class of algebras called characteristically nilpotent among four-dimensional associative algebras.

History

Received: March 9, 2016
Revised: November 10, 2016
Published: February 19, 2017

AMS Classification, Key Words

AMS Subject Classification: 16D70
Key Words and Phrases: derivation, centroid, associative algebra, characteristically nilpotent

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

N. Jacobson, A note on automorphisms and derivations of Lie algebras, Proc. Amer. Math. Soc., 6(2), (1955), 281-283.

2

J. Dixmier, W.G. Lister, Derivations of nilpotent Lie algebras, Proc. Amer. Math. Soc., 8 (1957), 155-158.

3

G. Leger, S. Togo, Characteristically nilpotent Lie algebras, Duke Math. J., 26(4), (1959), 623-628.

4

J. Tits, Sur les constantes de structure et le theorem dexistence des algebres de Lie semisimples, Publ. Math. I.H.E.S., 31(1), (1966), 21-58. https://dx.doi.org/10.1007/BF02684801.

5

B. Pierce, Linear Associative algebras, Amer. Math. Journal, (1881), 4(1) 97-229. https://www.jstor.org/stable/2369153.

6

O.C. Hazlett, On the classification and invariantive characterization of nilpotent algebras, American Journal of Mathematics, 38(2), (1916), 109-138. https://www.jstor.org/stable/2370262

7

G. Mazzola, The algebraic and geometric classification of associative algebras of dimension five, Manuscripta Math., 27(1), (1979), 81-–101. https://dx.doi.org/10.1007/BF01297739.

8

G. Mazzola, Generic finite schemes and Hochschild cocycles, Commentarii Mathematici Helvetici, 55(1), (1980), 267-293 . https://dx.doi.org/10.1007/BF02566686.

9

B. Poonen, Isomorphism types of commutative algebras of finite rank, Computational Arithmetic Geometry, 463(2008), 111-120.

10

I.S. Rakhimov, I.M. Rikhsiboev, W. Basri, Complete lists of low dimensional complex associative algebras, (2009). arXiv:0910.0932v1 [math.RA].

11

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.

12

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

13

M.A. Fiidow, I.S. Rakhimov, S.K. Said Hussain, Derivations and Centroids of Associative algebras. IEEE Proceedings of International Conference on Research and Education in Mathematics (ICREM7). (2015), 227-232. https://dx.doi.org/10.1109/ICREM.2015.7357059.

How to Cite?

DOI: 10.12732/ijpam.v112i4.1 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: 112
Issue: 4
Pages: 655 - 671

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

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

---