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
Falleh R. Al-Solamy1
and Edwin J. Beggs2
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
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.