After a long time looking for a solution in order to install JAva on a 64bits installation of Fedora 9, i've found one, and give it to you here (thx Andreia).
all the tutoz i've found until now didn't work. It's that the diference was made by the installation of the library libXtst.i386 and the creation of a nez directory for firefox plugins. Curtam !
#add i386 repository
#create and edit the configuration file of the repo
gedit /etc/yum.repos.d/fedora-i386.repo
#copy and paste those infomations in that file and save it
[fedora-i386]
name=Fedora $releasever - i386
failovermethod=priority
baseurl=http://download.fedora.redhat.com/pub/fedora/linux/releases/$releasever/Everything/i386/os/
mirrorlist=http://mirrors.fedoraproject.org/mirrorlist?repo=fedora-$releasever&arch=i386
enabled=1
gpgcheck=1
includepkgs=firefox
gpgkey=file:///etc/pki/rpm-gpg/RPM-GPG-KEY-fedora
#
[updates-i386]
name=Fedora $releasever - i386 - Updates
failovermethod=priority
baseurl=http://download.fedora.redhat.com/pub/fedora/linux/updates/$releasever/i386/
mirrorlist=http://mirrors.fedoraproject.org/mirrorlist?repo=updates-released-f$releasever&arch=i386
enabled=1
gpgcheck=1
includepkgs=firefox
gpgkey=file:///etc/pki/rpm-gpg/RPM-GPG-KEY-fedora
# remove the default java installation
yum -y erase java-1.6.0-openjdk java-1.0.6-openjdk-plugin
# remove the default Firefox installation (64bits)
yum -y erase firefox.x86_64
# install Firefox 32bits
yum -y install firefox.i386
# add this library
yum -y install libXtst.i386
# download java
www.java.com/en/download
escolher Linux RPM (self-extracting file) filesize: 18.32 MB
# install the .bin
chmod +x jre*
sh ./jre*
# make the links with firefox plugins
mkdir -p /usr/lib/firefox-3.0/plugins
ln-s /usr/java/jre*/plugins/i386/ns7/libjavaplugin_oji.so