TY - JOUR
T1 - Affine extensions of multiple conjugation quandles and augmented MCQ Alexander pairs
AU - Murao, Tomo
N1 - Funding Information:
The author would like to thank Atsushi Ishii for his valuable comments. The author was supported by JSPS KAKENHI Grant Number 18J10105 .
Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2020
Y1 - 2020
N2 - A multiple conjugation quandle is an algebra whose axioms are motivated from handlebody-knot theory. Any linear extension of a multiple conjugation quandle can be described by using a pair of maps called an MCQ Alexander pair. In this paper, we show that any affine extension of a multiple conjugation quandle can be described by using a quadruple of maps, called an augmented MCQ Alexander pair.
AB - A multiple conjugation quandle is an algebra whose axioms are motivated from handlebody-knot theory. Any linear extension of a multiple conjugation quandle can be described by using a pair of maps called an MCQ Alexander pair. In this paper, we show that any affine extension of a multiple conjugation quandle can be described by using a quadruple of maps, called an augmented MCQ Alexander pair.
KW - Affine extension
KW - Augmented MCQ Alexander pair
KW - Handlebody-knot
KW - Multiple conjugation quandle
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U2 - 10.1016/j.topol.2020.107531
DO - 10.1016/j.topol.2020.107531
M3 - Article
AN - SCOPUS:85098585057
SN - 0166-8641
JO - Topology and its Applications
JF - Topology and its Applications
M1 - 107531
ER -