Linear extensions of multiple conjugation quandles and MCQ Alexander pairs

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 multiple conjugation quandle is an algebra whose axioms are motivated from handlebody-knot theory.