Tree algebras: An algebraic axiomatization of intertwining vertex operators

Igor Kříž; Yang Xiu

Archivum Mathematicum (2012)

  • Volume: 048, Issue: 5, page 353-370
  • ISSN: 0044-8753

Abstract

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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 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 .

How to cite

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Kříž, Igor, and Xiu, Yang. "Tree algebras: An algebraic axiomatization of intertwining vertex operators." Archivum Mathematicum 048.5 (2012): 353-370. <http://eudml.org/doc/247244>.

@article{Kříž2012,
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 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 $\mathbb \{Q\}$.},
author = {Kříž, Igor, Xiu, Yang},
journal = {Archivum Mathematicum},
keywords = {vertex algebra; Riemann-Hilbert correspondence; D-module; KZ-equations; WZW-model; vertex algebra; Riemann-Hilbert correspondence; D-module; KZ-equations; WZW-model},
language = {eng},
number = {5},
pages = {353-370},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Tree algebras: An algebraic axiomatization of intertwining vertex operators},
url = {http://eudml.org/doc/247244},
volume = {048},
year = {2012},
}

TY - JOUR
AU - Kříž, Igor
AU - Xiu, Yang
TI - Tree algebras: An algebraic axiomatization of intertwining vertex operators
JO - Archivum Mathematicum
PY - 2012
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 048
IS - 5
SP - 353
EP - 370
AB - 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 $\mathbb {Q}$.
LA - eng
KW - vertex algebra; Riemann-Hilbert correspondence; D-module; KZ-equations; WZW-model; vertex algebra; Riemann-Hilbert correspondence; D-module; KZ-equations; WZW-model
UR - http://eudml.org/doc/247244
ER -

References

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