This is the moment when Joe Fernand will pop-up with an obscure HDMI-over-powerline solution I've never heard of
... but... to the best of my knowledge this is not currently possible and to be honest I think it is unlikely to be either due simly to the large difference between the bandwidth currently possible over power lines and what you'd need to take HDMI that route.
There are some wireless solutions released/on the way, but they are not cheap either.
I believe a few folk are looking at the HomePlug standard to deliver full AV over mains cables - though as we've not seen a reliable standard definition solution as yet HDMI and its buddy HDCP may be a while yet.
HDMI over single or twin Ethernet cables is now a daily requirement and pretty cost effective.
Wireless HDMI is just around the corner in the US - though not as yet in the UK/Europe and some of the systems are pretty costly.