We give explicit descriptions of the adjoint group of the Coxeter quandle associated with an arbitrary Coxeter group . The adjoint group turns out to be an intermediate group between and the corresponding Artin group , and it fits into a central extension of by a finitely generated free abelian group. We construct -cocycles of corresponding to the central extension. In addition, we prove that the commutator subgroup of the adjoint group is isomorphic to the commutator subgroup of . Finally, the root system associated with a Coxeter group turns out to be a rack. We prove that the adjoint group of is isomorphic to the adjoint group of .
"The adjoint group of a Coxeter quandle." Kyoto J. Math. 60 (4) 1245 - 1260, December 2020. https://doi.org/10.1215/21562261-2019-0061