2009/03/01 by Haisheng Li, Li, Haisheng
Mathematics · #17B68 #17B69 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.0903.0186
openalex publication_date 2009/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is a paper in a series to study vertex algebra-like structures arising from various algebras including quantum affine algebras and Yangians. In this paper, we develop a theory of what we call (weak) quantum vertex \F((t))-algebras with \F a field of characteristic zero and t a formal variable, and we give a conceptual construction of (weak) quantum vertex \F((t))-algebras and their modules. As an application, we associate weak quantum vertex \F((t))-algebras to quantum affine algebras, providing a solution to a problem posed by Frenkel and Jing. We also explicitly construct an example of quantum vertex \F((t))-algebras from a certain quantum βγ-system.