Hopf algebra extension of a Zamolochikov algebra and its double

Abstract

The particles with a scattering matrix R(x) are defined as operators ${\Phi }_i(z)$ satisfying the relation $R_{i,j}^{j^{\prime },i^{\prime }}(x_1/x_2){\Phi }_{i^{\prime }}(x_1){\Phi }_{j^{\prime }}(x_2)={\Phi }_i(x_2){\Phi }_j(x_1)$. The algebra generated by those operators is called a Zamolochikov algebra. We construct a new Hopf algebra by adding half of the FRTS construction of a quantum affine algebra with this R(x). Then we double it to obtain a new Hopf algebra such that the full FRTS construction of a quantum affine algebra is a Hopf subalgebra inside. Drinfeld realization of quantum affine algebras is included as an example. This is a further generalization of the constructions in q-alg/9608002.

arXiv comment9 pages Amslatex