On Classification of Quandles of Cyclic Type

被引：12

作者：

Kamada, Seiichi ^{[1
,2
]}

Tamaru, Hiroshi ^{[3
]}

Wada, Koshiro ^{[4
]}

机构：

[1] Osaka City Univ, Osaka, Japan

[2] Osaka City Univ, Dept Math, Osaka 5588585, Japan

[3] Hiroshima Univ, Dept Math, Higashihiroshima, Hiroshima 7398526, Japan

[4] Digital Solut Inc, Asaminami Ku, Hiroshima 7310122, Japan

来源：

TOKYO JOURNAL OF MATHEMATICS | 2016年 / 39卷 / 01期

关键词：

Finite quandles; two-point homogeneous quandles; quandles of cyclic type; 2-POINT HOMOGENEOUS QUANDLES; CARDINALITY; INVARIANTS; KNOTS;

D O I：

10.3836/tjm/1459367262

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study quandles of cyclic type, which form a particular subclass of finite quandles. The main result of this paper describes the set of isomorphism classes of quandles of cyclic type in terms of certain cyclic permutations. By using our description, we give a direct classification of quandles of cyclic type with cardinality up to 12.

引用

页码：157 / 171

页数：15

共 14 条

[1]

Carter J. S., 2012, INTRO LECT KNOT THEO, V46, P22

[2] Quandle cohomology and state-sum invariants of knotted curves and surfaces [J].

Carter, JS ;

Jelsovsky, D ;

Kamada, S ;

Langford, L ;

Saito, M .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 355 (10) :3947-3989

[3]

Fenn R., 1992, Journal of Knot Theory and Its Ramifications, V1, P343

[4] CANONICAL FORMS FOR OPERATION TABLES OF FINITE CONNECTED QUANDLES [J].

Hayashi, Chuichiro .

COMMUNICATIONS IN ALGEBRA, 2013, 41 (09) :3340-3349

[5] A G-FAMILY OF QUANDLES AND HANDLEBODY-KNOTS [J].

Ishii, Atsushi ;

Iwakiri, Masahide ;

Jang, Yeonhee ;

Oshiro, Kanako .

ILLINOIS JOURNAL OF MATHEMATICS, 2013, 57 (03) :817-838

[6] A CLASSIFYING INVARIANT OF KNOTS, THE KNOT QUANDLE [J].

JOYCE, D .

JOURNAL OF PURE AND APPLIED ALGEBRA, 1982, 23 (01) :37-65

[7]

KAMADA S., 2012, SPRINGER GENDAI SUGA, V16

[8] HOMOLOGY GROUPS OF SYMMETRIC QUANDLES AND COCYCLE INVARIANTS OF LINKS AND SURFACE-LINKS [J].

Kamada, Seiichi ;

Oshiro, Kanako .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 362 (10) :5501-5527

[9] On finite racks and quandles [J].

Lopes, P ;

Roseman, D .

COMMUNICATIONS IN ALGEBRA, 2006, 34 (01) :371-406

[10] Quandle cocycles from invariant theory [J].

Nosaka, Takefumi .

ADVANCES IN MATHEMATICS, 2013, 245 :423-438

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