Two-dimensional topological order and operator algebras
Yasuyuki Kawahigashi
Abstract
We review recent interactions between mathematical theory of two-dimensional topological order and operator algebras, particularly the Jones theory of subfactors. The role of representation theory in terms of tensor categories is emphasized. Connections to two-dimensional conformal field theory are also presented. In particular, we discuss anyon condensation, gapped domain walls and matrix product operators in terms of operator algebras.
Topics & Concepts
Operator algebraAnyonOperator (biology)MathematicsRepresentation theoryOrder (exchange)Conformal field theoryTensor productAlgebra over a fieldTopological algebraTopological quantum field theoryRepresentation (politics)Field (mathematics)Pure mathematicsOperator product expansionConformal mapPhysicsTopological spaceMathematical physicsMathematical analysisQuantum mechanicsTopological quantum computerQuantumEconomicsPolitical scienceTranscription factorGeneFinanceRepressorPoliticsLawBiochemistryChemistryAlgebraic structures and combinatorial modelsQuantum many-body systemsAdvanced Operator Algebra Research