TY - JOUR
T1 - Linear extensions of multiple conjugation quandles and MCQ Alexander pairs
AU - Murao, Tomo
N1 - Funding Information:
The author would like to thank Atsushi Ishii and Shosaku Matsuzaki for valuable discussions and making suggestions for improvement. The author was supported by JSPS KAKENHI Grant No. 18J10105.
Publisher Copyright:
© 2021 World Scientific Publishing Company.
PY - 2021/3
Y1 - 2021/3
N2 - A quandle is an algebra whose axioms are motivated from knot theory. A linear extension of a quandle can be described by using a pair of maps called an Alexander pair. In this paper, we show that a linear extension of a multiple conjugation quandle can be described by using a pair of maps called an MCQ Alexander pair, where a MCQ is an algebra whose axioms are motivated from handlebody-knot theory.
AB - A quandle is an algebra whose axioms are motivated from knot theory. A linear extension of a quandle can be described by using a pair of maps called an Alexander pair. In this paper, we show that a linear extension of a multiple conjugation quandle can be described by using a pair of maps called an MCQ Alexander pair, where a MCQ is an algebra whose axioms are motivated from handlebody-knot theory.
KW - MCQ Alexander pair
KW - Multiple conjugation quandle
KW - handlebody-knot
KW - linear extension
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U2 - 10.1142/S0219498821500456
DO - 10.1142/S0219498821500456
M3 - Article
AN - SCOPUS:85103922693
SN - 0219-4988
VL - 20
JO - Journal of Algebra and Its Applications
JF - Journal of Algebra and Its Applications
IS - 3
M1 - 500456
ER -