%0 Journal Article %T A $G$-family of quandles and handlebody-knots %A Atsushi Ishii %A Masahide Iwakiri %A Yeonhee Jang %A Kanako Oshiro %J Mathematics %D 2012 %I arXiv %X We introduce the notion of a $G$-family of quandles which is an algebraic system whose axioms are motivated by handlebody-knot theory, and use it to construct invariants for handlebody-knots. Our invariant can detect the chiralities of some handlebody-knots including unknown ones. %U http://arxiv.org/abs/1205.1855v1