Is that green magic that the lady elf uses in the game at all?
It's just a cinematic and doesn't represent actual in-game play. There are several other skills, armor, and effects that you see in that cinematic that aren't available either.
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I'd like to note on this, I actually think this is a future class for reasons I'll list here.
First off it's not a warden or sorc. Its telekinesis which came from mysticism in oblivion obviously looking different (green telekinesis grabs to people and environment). Also she had a dome shield which was also a ability that sounds derived from mysticism.
These things really rule out other classes for sure wether it was the start of one class or not and I dont think it was.
On a side note. I've noticed ZOS is really branching out in classes showing off multiple types of dmg and utility. For example a DK being fire or poison, utilizing earth as well as having a dragon theme together. They havent touched down deep into all the schools of magic just yet, and some classes share those schools in a different way like sorc and warden having some conjuration. So it seems they want to touch down on everything and they aren't afraid to put multiple schools of magic in a class or reuse some of them like sorc, warden and necro having a form of conjuration.
I'd like to add to the second paragraph, with this last fact and that is did anyone notice the necromancer in one of the first trailer on the horse??? Same dude from the new trailer lol.
All I'm saying is stuff from the beginning trailers is totally possible