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Explore the main themes, entities and connections around Modular tensor category. Start with the topic map, then use the sections below for research and deeper semantic analysis.
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Definition
20 related topics
Constructions of modular tensor categories
25 related topics
Description
15 related topics
Overview
20 related topics
Key facts & relationships
High-confidence facts extracted from structured source data. Use them as anchors for further research.
Topics to explore
A structured outline of related entities, concepts and subtopics. Open any item to build a new map centered on it.Browse the full topic structure. Each item opens a new analysis centered on that subject.
Overview
- Monoidal category
- Topological quantum field theories Topological quantum field theory
- Conformal field theory
- Quantum algebra
- Greg Moore Greg Moore (physicist)
- Nathan Seiberg
- Rational conformal field theories Rational conformal field theory
- Quantum field theory
- Condensed matter physics
- Algebraic theory of topological quantum information
- Anyons
- Topological quantum phases of matter Topological order
- Semisimple Semi-simplicity
- Braided Braided monoidal category
- Fusion category
- Invariance Invariant (mathematics)
- Quantum groups Quantum group
- Representation theory
- Low-dimensional topology
- Manifold Manifold (mathematics)
Description
- Igor Frenkel
- Vladimir Turaev
- Modular group
- Categories Category theory
- Tensors Tensor
- Spherical Spherical category
- Deligne Pierre Deligne
- Ribbon Ribbon category
- Bruguières modularity theorem
- Modular group representation
- Skeletonization Skeletonization of fusion categories
- Verlinde formula
- Rank-finiteness theorem Rank-finiteness for fusion categories
- Schauenburg-Ng theorem
- Müger's theorem
Definition
- Linear Preadditive category
- Enriched Enriched category
- Rigid category
- Pivotal Pivotal category
- Natural isomorphism Natural transformation
- Equivalence Equivalence of categories
- Functor
- Isomorphism
- Morphisms Morphism
- Natural number
- Quantum mechanical Quantum mechanics
- Joint excitation Fusion of anyons
- String operators Wilson loop
- Antiparticles
- Topological charge Topological quantum number
- Superselection sectors Superselection
- 2-vector space Higher-dimensional algebra
- Abelian Abelian category
- Semisimple Semisimple category
- Simple objects Schur's lemma
Relationship to topological quantum field theory
- Reshetikhin–Turaev construction Reshetikhin–Turaev invariant
- Nicolai Reshetikhin
- Edward Witten
- Bijection
- Anomalous Anomaly (physics)
- 2-category Strict 2-category
Relationship to rational conformal field theory
- Chiral Chirality (physics)
- Symmetric Symmetric algebra
- Frobenius Frobenius algebra
- Algebra object Group object
- Vertex operator algebras Vertex operator algebra
- Category of representations
Constructions of modular tensor categories
- Finite group theory Finite group
- Group Group (mathematics)
- Drinfeld center Center (category theory)
- Graded (complex) vector spaces Graded vector space
- Morita equivalence
- Group cohomology
- Circle group
- Gauge group Gauge theory
- Robbert Dijkgraaf
- Lagrangian Lagrangian (field theory)
- Kitaev Alexei Kitaev
- Quantum double model
- Compact Compact group
- Simple Simple Lie group
- Simply-connected Simply connected space
- Lie group
- Associated Lie group–Lie algebra correspondence
- Lie algebra
- Dual Coxeter number
- Cartan matrix
- Chern–Simons theory
- Weak Hopf algebra
- Tannaka–Krein duality
- Quasitriangular Quasitriangular Hopf algebra
- Subfactors Subfactor
Advanced semantic analysis
Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.
Map overview Semantic statistics
Number of nodes, edges, triples, density and central hubs. Use it to gauge the size and connectivity of the map.Modular tensor category
Nodes99
Edges98
Triples93
Avg. degree1.98
Density0.020202
Components1
How this topic connects Entity context
Quick relationship hints grouped by predicate. Useful for spotting recurring semantic connections around the current entity.See the strongest relationship patterns around the current topic before diving into the raw triples.
Modular tensor category
Top relations
related to From quantum groups · 15
Modular tensor category → Associated, Cartan, Chern, Chern-Simons, Coxeter, Edward Witten, For, From, It, Lie, On, Reshetikhin-Turaev, Simons, The, Witten's
related to From weak Hopf algebras · 15
Modular tensor category → Adding, For, Hopf, In, It, Kitaev, Krein, On, Reshetikhin-Turaev, Takahiro Hayashi, Tannaka, There, These, Vec, Weak Hopf
related to From finite groups · 14
Modular tensor category → Alternatively, Cochains, Drinfeld, In, It, More, Morita, One, Rep, Taking, That, There, This, Vec
related to Relationship to rational conformal field theory · 14
Modular tensor category → After, Christoph Schweigert, Frobenius, Greg Moore, Ingo Runkel, Jürgen Fuchs, Moore, Moore-Seiberg, Nathan Seiberg, Seiberg, The, There, This, When
related to Description · 12
Modular tensor category → Deligne's, His, Igor Frenkel, In, Modular, One, S-matrix, The, The Bruguières, There, Thus, Vladimir Turaev
related to Relationship to topological quantum field theory · 12
Modular tensor category → Edward Witten's, End, Here, In, Nicolai Reshetikhin, Reshetikhin, Reshetikhin-Turaev, The, The Reshetikhin-Turaev, This, Turaev, Vladimir Turaev
related to Relationship to other notions · 6
Modular tensor category → Kapranov, Often, That, There, Vec, Voevodsky
related to Definition · 3
Modular tensor category → That, The, Vec
is a · 2
Modular tensor category → braided spherical fusion category with non-degenerate braiding, rigid
Important terminology Word statistics
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Important terminology
modular displaystyle tensor category categories theory mathcal quantum field topological group structure fusion spherical conformal mathbb defined construction algebra representation
Entity relationships Subject–Predicate–Object triples
Extracted RDF-like relationships with confidence and source. The table includes structured facts and lower-confidence contextual relations.| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Modular tensor category | is a | rigid | 0.90 | text |
| Modular tensor category | is a | braided spherical fusion category with non-degenerate braiding | 0.90 | text |
| Modular tensor category | related to Definition | That | 0.60 | section |
| Modular tensor category | related to Definition | Vec | 0.60 | section |
| Modular tensor category | related to Definition | The | 0.60 | section |
| Modular tensor category | related to Description | The | 0.60 | section |
| Modular tensor category | related to Description | Igor Frenkel | 0.60 | section |
| Modular tensor category | related to Description | Vladimir Turaev | 0.60 | section |
| Modular tensor category | related to Description | His | 0.60 | section |
| Modular tensor category | related to Description | There | 0.60 | section |
| Modular tensor category | related to Description | One | 0.60 | section |
| Modular tensor category | related to Description | In | 0.60 | section |
No triples extracted yet.
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