start-ver=1.4
cd-journal=joma
no-vol=12
cd-vols=
no-issue=
article-no=
start-page=123
end-page=133
dt-received=
dt-revised=
dt-accepted=
dt-pub-year=2006
dt-pub=20060824
dt-online=
en-article=
kn-article=
en-subject=
kn-subject=
en-title=
kn-title=Some classical views on the parameters of the Grothendieck-Teichm?eller group
en-subtitle=
kn-subtitle=
en-abstract=
kn-abstract=<p>We present two new formulas concerning behaviors of the standard parameters of the Grothendieck-Teichm?ller group GT , and discuss their relationships with classical mathematics. First, considering a non-Galois etale cover of P<sub>1</sub> {0 1 infinity} of degree 4, we present a newtype equation satisfied by the Galois image in GT . Second, a certain equation in GL <sub>2</sub> (Z||Z<sub>2</sub> ) satisfied by every element of GT is derived as an application of (profinite) free differential calculus.</p>

en-copyright=
kn-copyright=

en-aut-name=NakamuraHiroaki
en-aut-sei=Nakamura
en-aut-mei=Hiroaki
kn-aut-name=
kn-aut-sei=
kn-aut-mei=
aut-affil-num=1
ORCID=

affil-num=1
en-affil=
kn-affil=Okayama University
en-keyword=Grothendieck-Teichm?eller group
kn-keyword=Grothendieck-Teichm?eller group
en-keyword=Belyi function
kn-keyword=Belyi function
en-keyword=modular function
kn-keyword=modular function
END