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