The fusion algebra of bimodule categories

DOI10.1007/s10485-007-9102-7zbMath1154.18003arXivmath/0701223OpenAlexW2149915493MaRDI QIDQ2426129

Christoph Schweigert, Jürgen Fuchs, Ingo Runkel

Publication date: 21 April 2008

Published in: Applied Categorical Structures (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701223

zbMATH Keywords

modular tensor categoryfusion algebrabimodule categorycomplexified Grothendieck ring

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40)

Related Items

Lorentzian dynamics and factorization beyond rationality, Pointed Drinfeld center functor, Tensor Categories for Vertex Operator Superalgebra Extensions, RCFT with defects: Factorization and fundamental world sheets, KRAMERS–WANNIER DUALITIES FOR WZW THEORIES AND MINIMAL MODELS, Rigidity and defect actions in Landau-Ginzburg models, Topological defect lines and renormalization group flows in two dimensions, Morita classes of algebras in modular tensor categories, A monoidal category for perturbed defects in conformal field theory, Some remarks on defects and T-duality, On representing some lattices as lattices of intermediate subfactors of finite index, Dualizable tensor categories

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Duality and defects in rational conformal field theory
• Uniqueness of open/closed rational CFT with given algebra of open states
• New braided endomorphisms from conformal inclusions
• Modular invariants, graphs and \(\alpha\)-induction for nets of subfactors. I
• A duality for Hopf algebras and for subfactors. I
• Braided tensor categories
• Galois modular invariants of WZW models
• Module categories, weak Hopf algebras and modular invariants
• Subfactor realisation of modular invariants
• The structure of sectors associated with Longo-Rehren inclusions. I: General theory
• TFT construction of RCFT correlators. I: Partition functions
• On a \(q\)-analogue of the McKay correspondence and the ADE classification of \(\mathfrak{sl}_{2}\) conformal field theories
• From subfactors to categories and topology. I: Frobenius algebras in and Morita equivalence of tensor categories
• On \(\alpha\)-induction, chiral generators and modular invariants for subfactors
• Conformal orbifold theories and braided crossed \(G\)-categories
• On fusion categories.
• Correspondences of ribbon categories
• NETS OF SUBFACTORS
• Quantum invariants of knots and 3-manifolds
• Generalised twisted partition functions
• The many faces of Ocneanu cells
• Boundary conformal field theory and fusion ring representations