Advances in Mathematical Physics
Volume 2010 (2010), Article ID 389091, 21 pages
doi:10.1155/2010/389091
Research Article

On the Deformation Theory of Structure Constants for Associative Algebras

B. G. Konopelchenko

Dipartimento di Fisica, Universita del Salento and INFN, Sezione di Lecce, 73100 Lecce, Italy

Received 5 October 2009; Revised 30 March 2010; Accepted 16 May 2010

Academic Editor: Alexander P. Veselov

Copyright © 2010 B. G. Konopelchenko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

An algebraic scheme for constructing deformations of structure constants for associative algebras generated by deformation driving algebras (DDAs) is discussed. An ideal of left divisors of zero plays a central role in this construction. Deformations of associative three-dimensional algebras with the DDA being a three-dimensional Lie algebra and their connection with integrable systems are studied.