Geodesic
Tree algebras: An algebraic axiomatization of intertwining vertex operators
Archivum mathematicum, Tome 48 (2012) no. 5, pp. 353-370.

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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 $\mathbb{Q}$.
DOI : 10.5817/AM2012-5-353
Classification : 17B69, 35Q15, 81T40
Keywords: vertex algebra; Riemann-Hilbert correspondence; D-module; KZ-equations; WZW-model 
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     title = {Tree algebras: {An} algebraic axiomatization of intertwining vertex operators},
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Kriz, Igor; Xiu, Yang. Tree algebras: An algebraic axiomatization of intertwining vertex operators. Archivum mathematicum, Tome 48 (2012) no. 5, pp. 353-370. doi : 10.5817/AM2012-5-353. http://geodesic.mathdoc.fr/articles/10.5817/AM2012-5-353/

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