Classification of Metaplectic Fusion Categories

被引：1
|
作者：
Ardonne, Eddy [1 ]
Finch, Peter E. [2 ]
Titsworth, Matthew [3 ]
机构：
[1] Stockholm Univ, Albanova Univ Ctr, Dept Phys, SE-10691 Stockholm, Sweden
[2] Leibniz Univ Hannover, Inst Theoret Phys, Appelstr 2, D-30167 Hannover, Germany
[3] Univ Texas Dallas, Dept Phys, Richardson, TX 75080 USA
来源：
SYMMETRY-BASEL | 2021年 / 13卷 / 11期
基金：
瑞典研究理事会;
关键词：
fusion category; metaplectic anyons; gauge invariants; MODULAR CATEGORIES; EQUIVALENCE; ALGEBRAS;
D O I：
10.3390/sym13112102
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
In this paper, we study a family of fusion and modular systems realizing fusion categories Grothendieck equivalent to the representation category for so(2p + 1)(2). These categories describe non-abelian anyons dubbed 'metaplectic anyons'. We obtain explicit expressions for all the F- and R-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.
引用
收藏
页数：22
相关论文
共 50 条
  • [1] Classification of metaplectic modular categories
    Ardonne, Eddy
    Cheng, Meng
    Rowell, Eric C.
    Wang, Zhenghan
    JOURNAL OF ALGEBRA, 2016, 466 : 141 - 146
  • [2] Dimension as a quantum statistic and the classification of metaplectic categories
    Bruillard, Paul
    Gustafson, Paul
    Plavnik, Julia Yael
    Rowell, Eric C.
    TOPOLOGICAL PHASES OF MATTER AND QUANTUM COMPUTATION, 2020, 747 : 89 - 113
  • [3] Integral metaplectic modular categories
    Deaton, Adam
    Gustafson, Paul
    Mavrakis, Leslie
    Rowell, Eric C.
    Poltoratski, Sasha
    Timmerman, Sydney
    Warren, Benjamin
    Zhang, Qing
    JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2020, 29 (05)
  • [4] On the classification of certain fusion categories
    Jordan, David
    Larson, Eric
    JOURNAL OF NONCOMMUTATIVE GEOMETRY, 2009, 3 (03) : 481 - 499
  • [5] On Metaplectic Modular Categories and Their Applications
    Matthew B. Hastings
    Chetan Nayak
    Zhenghan Wang
    Communications in Mathematical Physics, 2014, 330 : 45 - 68
  • [6] On Metaplectic Modular Categories and Their Applications
    Hastings, Matthew B.
    Nayak, Chetan
    Wang, Zhenghan
    COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2014, 330 (01) : 45 - 68
  • [7] Classification of fusion categories of dimension pq
    Etingof, P
    Gelaki, S
    Ostrik, V
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2004, 2004 (57) : 3041 - 3056
  • [8] METAPLECTIC CATEGORIES, GAUGING AND PROPERTY F
    Gustafson, Paul
    Rowell, Eric C.
    Ruan, Yuze
    TOHOKU MATHEMATICAL JOURNAL, 2020, 72 (03) : 411 - 424
  • [9] Morita equivalence methods in classification of fusion categories
    Nikshych, Dmitri
    HOPF ALGEBRAS AND TENSOR CATEGORIES, 2013, 585 : 289 - 325
  • [10] ON THE CLASSIFICATION OF POINTED FUSION CATEGORIES UP TO WEAK MORITA EQUIVALENCE
    Uribe, Bernardo
    PACIFIC JOURNAL OF MATHEMATICS, 2017, 290 (02) : 437 - 466
12345