Markov traces and II\(_ 1\) factors in conformal field theory

DOI10.1007/BF02352496zbMath0760.57002OpenAlexW2050865238MaRDI QIDQ1180978

Jan de Boer, Jacob K. Goeree

Publication date: 27 June 1992

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02352496

zbMATH Keywords

knot invariantMarkov traceduality equations of Moore and SeibergRational Conformal Field Theory

Mathematics Subject Classification ID

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fusion rules and modular transformations in 2D conformal field theory
• Classical and quantum conformal field theory
• On a certain value of the Kauffman polynomial
• Index of subfactors and statistics of quantum fields. II: Correspondences, braid group statistics and Jones polynomial
• Braiding matrices, modular transformations and topological field theories in \(2+1\) dimensions
• Action of discrete amenable groups on von Neumann algebras
• State models and the Jones polynomial
• Infinite conformal symmetry in two-dimensional quantum field theory
• Quantum field theory and the Jones polynomial
• The operator algebra of orbifold models
• Duality and quantum groups
• Classification of injective factors. Cases \(\mathrm{II}_1\), \(\mathrm{II}_\infty\), \(\mathrm{III}_\lambda\), \(\lambda\neq 1\)
• Index of subfactors and statistics of quantum fields. I
• Superselection sectors with braid group statistics and exchange algebras
• Index for subfactors
• On rings of operators. IV
• G_N ⊗ G_L/G_N+L CONFORMAL FIELD THEORIES AND THEIR MODULAR INVARIANT PARTITION FUNCTIONS
• A polynomial invariant for knots via von Neumann algebras
• On Knots. (AM-115)
• NOTES ON SUBFACTORS AND STATISTICAL MECHANICS
• Number fields
• Modular invariance and the fusion algebra

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