Tree Algebras: An algebraic axiomatization of intertwining vertex operators

2011/02/09 by Igor Kříž, Yang Xiu, Kriz, Igor +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1102.2007

openalex publication_date 2011/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe a completely algebraic axiom system for intertwining operators of vertex algebra modules, using algebraic flat connections, thus formulating the concept of a \em tree algebra. Using the Riemann-Hilbert correspondence, we further prove that a vertex tensor category in the sense of Huang and Lepowsky gives rise to a tree algebra over \C. We also show that the chiral WZW model of a simply connected simple compact Lie group gives rise to a tree algebra over \Q.

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