FUSION RULES ON A PARAMETRIZED SERIES OF GRAPHS

被引：1

作者：

Asaeda, Marta ^{[1
]}

Haagerup, Uffe ^{[2
]}

机构：

[1] Univ Calif Riverside, Dept Math, Riverside, CA 92521 USA

[2] Univ Copenhagen, Dept Math Sci, DK-2100 Copenhagen, Denmark

来源：

PACIFIC JOURNAL OF MATHEMATICS | 2011年 / 253卷 / 02期

关键词：

fusion algebra; operator algebra; subfactor; PRINCIPAL GRAPHS; SUBFACTORS;

D O I：

10.2140/pjm.2011.253.257

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A series of pairs of graphs (Gamma(k), Gamma'(k)), k = 0, 1, 2, ... , has been considered as candidates for dual pairs of principal graphs of subfactors of small Jones index above 4 and it has recently been proved that the pair (Gamma(k), Gamma'(k)) comes from a subfactor if and only if k = 0 or k = 1. We show that nevertheless there exists a unique fusion system compatible with this pair of graphs for all nonnegative integers k.

引用

页码：257 / 288

页数：32

共 9 条

[1]

Asaeda M, 1999, COMMUN MATH PHYS, V202, P1, DOI 10.1007/s002200050574

[2] Galois groups and an obstruction to principal graphs of subfactors [J].

Asaeda, Marta .

INTERNATIONAL JOURNAL OF MATHEMATICS, 2007, 18 (02) :191-202

[3] On Haagerup's List of Potential Principal Graphs of Subfactors [J].

Asaeda, Marta ;

Yasuda, Seidai .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2009, 286 (03) :1141-1157

[4] Constructing the extended Haagerup planar algebra [J].

Bigelow, Stephen ;

Morrison, Scott ;

Peters, Emily ;

Snyder, Noah .

ACTA MATHEMATICA, 2012, 209 (01) :29-82

[5]

DELAHARPE P, 1987, CR ACAD SCI I-MATH, V305, P733

[6]

Erdelyi A., 1981, HIGHER TRANSCENDENTA, V2

[7]

HAAGERUP U., 1994, Subfactors (Kyuzeso, 1993), P1

[8] APPLICATION OF FUSION RULES TO CLASSIFICATION OF SUBFACTORS [J].

IZUMI, M .

PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 1991, 27 (06) :953-994

[9] ON THE NON-OCCURRENCE OF THE COXETER GRAPHS BETA(2N+1), D(2N+1) AND E(7) AS THE PRINCIPAL GRAPH OF AN INCLUSION OF II(1)-FACTORS [J].

SUNDER, VS ;

VIJAYARAJAN, AK .

PACIFIC JOURNAL OF MATHEMATICS, 1993, 161 (01) :185-200

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