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Title: Tree algebras: An algebraic axiomatization of intertwining vertex operators (English)
Author: Kriz, Igor
Author: Xiu, Yang
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 48
Issue: 5
Year: 2012
Pages: 353-370
Summary lang: English
Category: math
Summary: We describe a completely algebraic axiom system for intertwining operators of vertex algebra modules, using algebraic flat connections, thus formulating the concept of a 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 $\mathbb{C}$. We also show that the chiral WZW model of a simply connected simple compact Lie group gives rise to a tree algebra over $\mathbb{Q}$. (English)
Keyword: vertex algebra
Keyword: Riemann-Hilbert correspondence
Keyword: D-module
Keyword: KZ-equations
Keyword: WZW-model
MSC: 17B69
MSC: 35Q15
MSC: 81T40
idMR: MR3007618
DOI: 10.5817/AM2012-5-353
Date available: 2012-12-17T14:01:18Z
Last updated: 2013-09-19
Stable URL:
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