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Modular tensor category: Definition, Constructions of modular tensor categories & Description

A modular tensor category (or modular fusion category) is a type of monoidal category that plays a role in the areas of topological quantum field theory, conformal field theory, and quantum algebra. Modular tensor categories were introduced in 1989 by the physicists Greg Moore and Nathan Seiberg in the context of rational conformal field theory. In the…

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Modular tensor category topic overview

The analysis highlights Definition, Constructions of modular tensor categories and Description as prominent areas in the source structure around Modular tensor category.

Related topics
92
Source areas
6
Connected nodes
98
Extracted relationships
93
Concept neighborhoods
43
Bridge connections
98

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Constructions of modular tensor categories · 25 topics
Definition · 20 topics
Overview · 20 topics
Description · 15 topics
Relationship to rational conformal field theory · 6 topics
Relationship to topological quantum field theory · 6 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Description

Definition

Relationship to topological quantum field theory

Relationship to rational conformal field theory

Constructions of modular tensor categories

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.

How Modular tensor category connects Entity context

The extracted context around Modular tensor category shows recurring relationship patterns in the source. For example, Modular tensor category → Associated, Cartan, Chern, Chern-Simons, Coxeter, Edward Witten, For, From, It, Lie, On, Reshetikhin-Turaev, Simons, The, Witten's Another extracted example is Modular tensor category → Adding, For, Hopf, In, It, Kitaev, Krein, On, Reshetikhin-Turaev, Takahiro Hayashi, Tannaka, There, These, Vec, Weak Hopf. Use these groups to spot repeated connection types before inspecting the individual relationships.

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

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

modular displaystyle tensor category categories theory mathcal quantum field topological group structure fusion spherical conformal mathbb defined construction algebra representation

Modular tensor category relationships Subject–Predicate–Object triples

TTTA extracted 93 structured relationships around Modular tensor category. Examples in this analysis include Modular tensor category → is a → rigid and Modular tensor category → is a → braided spherical fusion category with non-degenerate braiding. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Modular tensor categoryis arigid0.90text
Modular tensor categoryis abraided spherical fusion category with non-degenerate braiding0.90text
Modular tensor categoryrelated to DefinitionThat0.60section
Modular tensor categoryrelated to DefinitionVec0.60section
Modular tensor categoryrelated to DefinitionThe0.60section
Modular tensor categoryrelated to DescriptionThe0.60section
Modular tensor categoryrelated to DescriptionIgor Frenkel0.60section
Modular tensor categoryrelated to DescriptionVladimir Turaev0.60section
Modular tensor categoryrelated to DescriptionHis0.60section
Modular tensor categoryrelated to DescriptionThere0.60section
Modular tensor categoryrelated to DescriptionOne0.60section
Modular tensor categoryrelated to DescriptionIn0.60section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Modular tensor category bring nearby vocabulary together. In this analysis, examples include Tensor, Categories and Category. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Modular tensor category
    • Tensor
    • Categories
    • Category
    • Modular
    • Quantum
    • Theory
    • Field
    • Topological
    • Fusion
    • Construction
    • Displaystyle
    • Group
  • modular tensor category
    • Tensor
    • Categories
    • Category
    • Modular
    • Displaystyle
    • Quantum
    • Theory
    • Fusion
    • Field
    • Mathcal
    • Topological
    • Spherical
  • monoidal category
    • Modular
    • Displaystyle
    • Tensor
    • Fusion
    • Mathcal
    • -linear
    • Spherical
    • Algebra
    • Defined
    • Mathbb
    • Weak
    • Representation
  • topological quantum field theories
    • Theory
    • Conformal
    • Topological
    • Rational
    • Quantum
    • Categories
    • Group
    • Construction
    • Modular
    • Tensor
    • Introduced
    • Data
  • conformal field theory
    • Rational
    • Theory
    • Conformal
    • Field
    • Topological
    • Quantum
    • Categories
    • Data
    • Construction
    • Modular
    • Tensor
    • Introduced
  • quantum algebra
    • Topological
    • Theory
    • Hopf
    • Categories
    • Representation
    • Group
    • Weak
    • Construction
    • Every
    • Tensor
    • Monoidal
    • Category
  • rational conformal field theories
    • Rational
    • Theory
    • Conformal
    • Field
    • Topological
    • Quantum
    • Data
    • Modular
    • Categories
    • Tensor
    • Construction
    • Introduced
  • quantum field theory
    • Theory
    • Conformal
    • Topological
    • Rational
    • Quantum
    • Categories
    • Group
    • Construction
    • Modular
    • Tensor
    • Introduced
    • Data

Connections between topic areas Semantic bridges

For Modular tensor category, one of the stronger structural bridges in this analysis connects Modular tensor category with Constructions of modular tensor categories. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Modular tensor categoryConstructions of modular tensor categories · splits 73 ⟂ 26
Modular tensor categoryOverview · splits 78 ⟂ 21
Modular tensor categoryDefinition · splits 78 ⟂ 21
Modular tensor categoryDescription · splits 83 ⟂ 16
Modular tensor categoryRelationship to topological quantum field theory · splits 92 ⟂ 7
Modular tensor categoryRelationship to rational conformal field theory · splits 92 ⟂ 7

Map overview Semantic statistics

Modular tensor category

Nodes99
Edges98
Triples93
Avg. degree1.98
Density0.020202
Components1

Source & methodology

TTTA analyzes the structure around Modular tensor category to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Definition, Constructions of modular tensor categories & Description, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Modular tensor category · EN edition · Analysis: TopicsToTalkAbout

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