Braided Subfactors, Spectral Measures, Planar algebras and Calabi-Yau algebras associated to SU (3) modular invariants
نویسندگان
چکیده
Braided subfactors of von Neumann algebras provide a framework for studying two dimensional conformal field theories and their modular invariants. We review this in the context of SU(3) conformal field theories through corresponding SU(3) braided subfactors and various subfactor invariants including spectral measures for the nimrep graphs, A2-planar algebras and almost Calabi-Yau algebras.
منابع مشابه
On the homology of almost Calabi-Yau algebras associated to SU (3) modular invariants
We compute the Hochschild homology and cohomology, and cyclic homology, of almost Calabi-Yau algebras for SU(3) ADE graphs. These almost Calabi-Yau algebras are a higher rank analogue of the pre-projective algebras for Dynkin diagrams, which are SU(2)-related constructions. The Hochschild (co)homology and cyclic homology of A can be regarded as invariants for the braided subfactors associated t...
متن کاملCritical Phenomena, Modular Invariants and Operator Algebras
We review the framework subfactors provide for understanding modular invariants. We discuss the structure of a generalized Longo-Rehren subfactor and the relationship between the coupling matrices of such subfactors, modular invariance and local extensions. We relate results of Kostant, in the context of the McKay correspondence for finite subgroups of SU (2), to subfactors. A direct proof of h...
متن کاملOcneanu Cells and Boltzmann Weights for the SU (3) ADE Graphs
We determine the cells, whose existence has been announced by Ocneanu, on all the candidate nimrep graphs except E 4 proposed by di Francesco and Zuber for the SU(3) modular invariants classified by Gannon. This enables the Boltzmann weights to be computed for the corresponding integrable statistical mechanical models and provide the framework for studying corresponding braided subfactors to re...
متن کاملSU (3)-Goodman-de la Harpe-Jones subfactors and the realisation of SU (3) modular invariants
We complete the realisation by braided subfactors, announced by Ocneanu, of all SU(3)-modular invariant partition functions previously classified by Gannon.
متن کاملDeformed Calabi-yau Completions
We define and investigate deformed n-Calabi-Yau completions of homologically smooth differential graded (=dg) categories. Important examples are: deformed preprojective algebras of connected non Dynkin quivers, Ginzburg dg algebras associated to quivers with potentials and dg categories associated to the category of coherent sheaves on the canonical bundle of a smooth variety. We show that defo...
متن کامل