I first had a go at learning Swedish more than 40 years ago (I thought it was time I did a little revision!) -- and I seem to remember that, even then, the very first lesson featured a key (en nyckel) and an ant (en myra). Perhaps they were just trying to teach the pronunciation of the letter 'y'!
I'm guessing grammatically closer translations are "The ant lives" or "The ant is living". Would these not be more instructive than "the ant is alive"?
Do you have an adjective in Swedish for living that would allow you to say the exact equivalent of "the ant is alive", or would you always "Myran lever"?