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The adjoint group of a Coxeter quandle

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Title: The adjoint group of a Coxeter quandle
Authors: Akita, Toshiyuki Browse this author
Issue Date: Dec-2020
Publisher: Duke University Press
Journal Title: Kyoto journal of mathematics
Volume: 60
Issue: 4
Start Page: 1245
End Page: 1260
Publisher DOI: 10.1215/21562261-2019-0061
Abstract: 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).
Type: article (author version)
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 秋田 利之

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