open access

https://hdl.handle.net/2115/80388

The adjoint group of a Coxeter quandle

英語

2020-12

Duke University Press

Kyoto journal of mathematics

60(4)

1245-1260

We give explicit descriptions of the adjoint group Ad(Q(w)) of the Coxeter quandle Q(w) associated with an arbitrary Coxeter group W. The adjoint group Ad(Q(w)) turns out to be an intermediate group between W and the corresponding Artin group A(w), and it fits into a central extension of W by a finitely generated free abelian group. We construct 2-cocycles of W corresponding to the central extension. In addition, we prove that the commutator subgroup of the adjoint group Ad(Q(w)) is isomorphic to the commutator subgroup of W. Finally, the root system Phi(w) associated with a Coxeter group W turns out to be a rack. We prove that the adjoint group Ad(Phi(w)) of Phi(w) is isomorphic to the adjoint group of Q(w).

学術雑誌論文

Accepted Manuscript

2156-2261