Ding-Iohara algebras and quantum vertex algebras

2017/06/09 by Haisheng Li, Li, Haisheng, Shaobin Tan +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1706.03636

openalex publication_date 2017/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ϕ-coordinated modules for these quantum vertex algebras are associated to \widetildeA(g)-modules. Furthermore, we classify their irreducible ϕ-coordinated modules.

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• Double Yangians and quantum vertex algebras, I

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