Classification of Metaplectic Fusion Categories

In this paper, we study a family of fusion and modular systems realizing fusion categories Grothendieck equivalent to the representation category for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi...

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Autores principales:	Eddy Ardonne, Peter E. Finch, Matthew Titsworth
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	fusion category metaplectic anyons gauge invariants Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/3eb275166b7b4bdd92b2a2ac764b5fa8
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spelling	oai:doaj.org-article:3eb275166b7b4bdd92b2a2ac764b5fa82021-11-25T19:06:45ZClassification of Metaplectic Fusion Categories10.3390/sym131121022073-8994https://doaj.org/article/3eb275166b7b4bdd92b2a2ac764b5fa82021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2102https://doaj.org/toc/2073-8994In this paper, we study a family of fusion and modular systems realizing fusion categories Grothendieck equivalent to the representation category for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="fraktur">so</mi><msub><mrow><mo>(</mo><mn>2</mn><mi>p</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></msub></mrow></semantics></math></inline-formula>. These categories describe non-abelian anyons dubbed ‘metaplectic anyons’. We obtain explicit expressions for all the <i>F</i>- and <i>R</i>-symbols. Based on these, we conjecture a classification for their monoidal equivalence classes from an analysis of their gauge invariants and define a function which gives us the number of classes.Eddy ArdonnePeter E. FinchMatthew TitsworthMDPI AGarticlefusion categorymetaplectic anyonsgauge invariantsMathematicsQA1-939ENSymmetry, Vol 13, Iss 2102, p 2102 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	fusion category metaplectic anyons gauge invariants Mathematics QA1-939
spellingShingle	fusion category metaplectic anyons gauge invariants Mathematics QA1-939 Eddy Ardonne Peter E. Finch Matthew Titsworth Classification of Metaplectic Fusion Categories
description	In this paper, we study a family of fusion and modular systems realizing fusion categories Grothendieck equivalent to the representation category for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="fraktur">so</mi><msub><mrow><mo>(</mo><mn>2</mn><mi>p</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></msub></mrow></semantics></math></inline-formula>. These categories describe non-abelian anyons dubbed ‘metaplectic anyons’. We obtain explicit expressions for all the <i>F</i>- and <i>R</i>-symbols. Based on these, we conjecture a classification for their monoidal equivalence classes from an analysis of their gauge invariants and define a function which gives us the number of classes.
format	article
author	Eddy Ardonne Peter E. Finch Matthew Titsworth
author_facet	Eddy Ardonne Peter E. Finch Matthew Titsworth
author_sort	Eddy Ardonne
title	Classification of Metaplectic Fusion Categories
title_short	Classification of Metaplectic Fusion Categories
title_full	Classification of Metaplectic Fusion Categories
title_fullStr	Classification of Metaplectic Fusion Categories
title_full_unstemmed	Classification of Metaplectic Fusion Categories
title_sort	classification of metaplectic fusion categories
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/3eb275166b7b4bdd92b2a2ac764b5fa8
work_keys_str_mv	AT eddyardonne classificationofmetaplecticfusioncategories AT peterefinch classificationofmetaplecticfusioncategories AT matthewtitsworth classificationofmetaplecticfusioncategories
_version_	1718410272620675072

Classification of Metaplectic Fusion Categories

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