International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 12, Pages 701-718
doi:10.1155/S0161171202020197
A generalised hopf algebra for solitons
1Department of Mathematics, Faculty of Science, King Abdul Aziz University, P.O. Box 80015, Jeddah 21589, Saudi Arabia
2Department of Mathematics, University of Wales Swansea, Wales, Swansea SA2 8PP, UK
Received 17 April 2001; Revised 22 October 2001
Copyright © 2002 Falleh R. Al-Solamy and Edwin J. Beggs. 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
This paper considers a generalisation of the idea of a Hopf
algebra in which a commutative ring replaces the field in the
unit and counit. It is motivated by an example from the inverse
scattering formalism for solitons. We begin with the
corresponding idea for groups, where the concept of the identity
is altered.