Hopf algebra extension of a Zamolochikov algebra and its double

Jintai Ding

doi:10.1063/1.532951

Hopf algebra extension of a Zamolochikov algebra and its double

Jintai Ding^*

^*Corresponding author for this work

University of Cincinnati

Research output: Contribution to journal › Article › peer-review

Abstract

The particles with a scattering matrix R(x) are defined as operators Φ_i(_z) satisfying the relation Σ_{i′ j′}R^j′,i′_i,j (x₁ / x₂)Φ_i′(x₁)Φ _j′(x₂) = Φ_i(x₂)Φ_j(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.

Original language	English
Pages (from-to)	4157-4164
Number of pages	8
Journal	Journal of Mathematical Physics
Volume	40
Issue number	8
DOIs	https://doi.org/10.1063/1.532951
Publication status	Published - Aug 1999
Externally published	Yes

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abstract = "The particles with a scattering matrix R(x) are defined as operators Φi(z) satisfying the relation Σi′ j′Rj′,i′i,j (x1 / x2)Φi′(x1)Φ j′(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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year = "1999",

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Hopf algebra extension of a Zamolochikov algebra and its double

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