1999•Journal of Mathematical PhysicsRequires access

Hopf algebra extension of a Zamolochikov algebra and its double

Jíntai Ding

Abstract

The particles with a scattering matrix R(x) are defined as operators Φi(z) satisfying the relation ∑i′,j′Ri,jj′,i′(x1/x2)Φi′(x1)Φj′(x2)=Φi(x2)Φj(x1). The algebra generated by those operators is called a Zamolochikov algebra. We construct a new Hopf algebra by adding half of the Faddeev–Reshetikhin–Takhtajan–Semenov-Tian-Shansky (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.

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Key concepts: Quantum affine algebra, Subalgebra, Filtered algebra, Mathematics, Hopf algebra, Cellular algebra, Algebra over a field, Division algebra