@sun No you can't. You can't use HDMI without their permission.
This is why it's important to keep standards like VGA alive -- because HDMI is a closed platform and at the end of the day they can keep people from using technology which they do not approve of with it
at least some of the patents are probably starting to expire
while there's probably some black-box reverse-engineering for some parts of it that will be protected, if they can prove you used any of their specs to do it they can probably get people in legal hot water for doing so given how tightly controlled it is.