On properties of commutative Alexander quandles

Yongju Bae; Seonmi Choi

doi:10.1142/S021821651460013X

On properties of commutative Alexander quandles

Yongju Bae
, Seonmi Choi

Kyungpook National University

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

An Alexander quandle M_t is an abelian group M with a quandle operation a∗b = ta + (1 - t)b where t is a group automorphism of the abelian group M. In this paper, we will study the commutativity of an Alexander quandle and introduce the relationship between Alexander quandles M_t and M_1-t determined by group automorphisms t and 1 - t, respectively.

Original language	English
Article number	1460013
Journal	Journal of Knot Theory and its Ramifications
Volume	23
Issue number	7
DOIs	https://doi.org/10.1142/S021821651460013X
State	Published - 25 Jun 2014

Keywords

Alexander quandle
group automorphism
Quandle

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10.1142/S021821651460013X

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title = "On properties of commutative Alexander quandles",

abstract = "An Alexander quandle Mt is an abelian group M with a quandle operation a∗b = ta + (1 - t)b where t is a group automorphism of the abelian group M. In this paper, we will study the commutativity of an Alexander quandle and introduce the relationship between Alexander quandles Mt and M1-t determined by group automorphisms t and 1 - t, respectively.",

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author = "Yongju Bae and Seonmi Choi",

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AU - Bae, Yongju

AU - Choi, Seonmi

PY - 2014/6/25

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N2 - An Alexander quandle Mt is an abelian group M with a quandle operation a∗b = ta + (1 - t)b where t is a group automorphism of the abelian group M. In this paper, we will study the commutativity of an Alexander quandle and introduce the relationship between Alexander quandles Mt and M1-t determined by group automorphisms t and 1 - t, respectively.

AB - An Alexander quandle Mt is an abelian group M with a quandle operation a∗b = ta + (1 - t)b where t is a group automorphism of the abelian group M. In this paper, we will study the commutativity of an Alexander quandle and introduce the relationship between Alexander quandles Mt and M1-t determined by group automorphisms t and 1 - t, respectively.

KW - Alexander quandle

KW - group automorphism

KW - Quandle

UR - https://www.scopus.com/pages/publications/84928361777

U2 - 10.1142/S021821651460013X

DO - 10.1142/S021821651460013X

M3 - Article

AN - SCOPUS:84928361777

SN - 0218-2165

VL - 23

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

IS - 7

M1 - 1460013

ER -

On properties of commutative Alexander quandles

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Keywords

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