7 papers
Quandles from group actions and a Cayley-type embedding theorem
Ryoya Kai
A quandle is an algebraic system that can be regarded as a generalization of the conjugation operation in groups. We study a quandle construction associated with group actions and…
Two-numbers and Euler characteristics for quandles
Ryoya Kai, Akira Kubo, Hiroshi Tamaru
Quandles can be regarded as generalizations of symmetric spaces. In the theory of symmetric spaces developed by Chen and Nagano, there is an interesting relationship between the tw…
A condition of admissibility for generalized Alexander quandles
Katsunori Arai, Keisuke Himeno, Ryoya Kai +1
A typical example of a quandle is the conjugation quandle. A quandle is said to be admissible if it is isomorphic to a conjugation quandle. We study the admissibility problem for q…
Detecting non-admissibility of quandles via colorings
Katsunori Arai, Ryoya Kai
A quandle is an algebraic system whose axioms are motivated by Reidemeister moves in knot theory. A typical example is a conjugation quandle arising from a group. A quandle is said…
Metrics for quandles
Kohei Iwamoto, Ryoya Kai, Yuya Kodama
A quandle is an algebraic system originating in knot theory, which can be regarded as a generalization of the conjugation of groups. This structure naturally defines two subgroups…
On the Euler characteristics for quandles
Ryoya Kai, Hiroshi Tamaru
A quandle is an algebraic system whose axioms generalize the algebraic structure of the point symmetries of symmetric spaces. In this paper, we give a definition of Euler character…
On the quandles of isometries of the hyperbolic 3-space
Ryoya Kai
A quandle is an algebraic structure whose axioms are related to the Reidemeister moves used in knot theory. In this paper, we investigate the conjugate quandle of the orientation-p…