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Ding-Iohara algebras and quantum vertex algebras

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arxiv 1706.03636 v1 pith:TO4SFMNC submitted 2017-06-09 math.QA

Haisheng Li , Shaobin Tan , Qing Wang This is my paper · ORCID
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keywords algebrasmodulesquantumvertexassociatedassociativecoordinatedding-iohara
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abstract

In this paper, we associate quantum vertex algebras to a certain family of associative algebras $\widetilde{\A}(g)$ which are essentially Ding-Iohara algebras. To do this, we introduce another closely related family of associative algebras $\A(h)$. The associated quantum vertex algebras are based on the vacuum modules for $\A(h)$, whereas $\phi$-coordinated modules for these quantum vertex algebras are associated to $\widetilde{A}(g)$-modules. Furthermore, we classify their irreducible $\phi$-coordinated modules.

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Cited by 1 Pith paper

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  1. On the quantum affine vertex algebra associated with trigonometric $R$-matrix

    math.QA 2019-08 conditional novelty 7.0 of 10

    Restricted modules for the quantum affine algebra in type A are equivalent, with submodule correspondence, to phi-coordinated modules for the Etingof-Kazhdan quantum affine vertex algebra with phi(z2,z0)=z2 e^{z0}.

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