The Witt group of non-degenerate braided fusion categories

被引：167
作者：
Davydov, Alexei [1 ]
Muger, Michael [2 ]
Nikshych, Dmitri [1 ]
Ostrik, Victor [3 ]
机构：
[1] Univ New Hampshire, Dept Math & Stat, Durham, NH 03824 USA
[2] Radboud Univ Nijmegen, Inst Math Astrophys & Particle Phys, NL-6525 ED Nijmegen, Netherlands
[3] Univ Oregon, Dept Math, Eugene, OR 97403 USA
来源：
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2013年 / 677卷
关键词：
VERTEX OPERATOR-ALGEBRAS; TENSOR CATEGORIES; HOPF-ALGEBRAS; REPRESENTATIONS; CLASSIFICATION; SUBFACTORS;
D O I：
10.1515/crelle.2012.014
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give a characterization of Drinfeld centers of fusion categories as non-degenerate braided fusion categories containing a Lagrangian algebra. Further we study the quotient of the monoid of non-degenerate braided fusion categories modulo the sub-monoid of the Drinfeld centers and show that its formal properties are similar to those of the classical Witt group.
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收藏
页码：135 / 177
页数：43
相关论文
共 46 条
  • [1] RATIONALITY IN CONFORMAL FIELD-THEORY
    ANDERSON, G
    MOORE, G
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1988, 117 (03) : 441 - 450
  • [2] BAIS FA, 1987, NUCL PHYS B, V279, P561, DOI 10.1016/0550-3213(87)90010-1
  • [3] Bakalov B., 2001, Translations of Mathematical Monographs
  • [4] Bezrukavnikov R., 2004, Adv. Stud. Pure Math., V40, P69, DOI [10.2969/aspm/04010069, DOI 10.2969/ASPM/04010069]
  • [5] COSET CONSTRUCTIONS AND EXTENDED CONFORMAL ALGEBRAS
    BOWCOCK, P
    GODDARD, P
    [J]. NUCLEAR PHYSICS B, 1988, 305 (04) : 685 - 709
  • [6] Bruguières A, 2000, MATH ANN, V316, P215, DOI 10.1007/s002080050011
  • [7] Bruguieres A., 2010, PREPRINT
  • [8] Cyclotomic Integers, Fusion Categories, and Subfactors
    Calegari, Frank
    Morrison, Scott
    Snyder, Noah
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2011, 303 (03) : 845 - 896
  • [9] Davydov A., 2010, PREPRINT
  • [10] Davydov A., 2007, PREPRINT
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