Can you sue your ex-employer for slander if they lie to the unemploy.office about the reason you were fired?

I worked for my co. for 11 years and a new manager came in who decided he didn't like me. I've always been a top producer, a hard worker and dedicated employee. I know I can't always expect everyone to like me in life, but I have never had anything but raving reviews from bosses/employers. He terminated me on the spot, with no doented proof of what he accused me of doing- and HR didn't stop him or even investigate it. He lied to his boss and HR - all based on he/said she/said - accused me of falsifying information- something I didn't do. Even the other co-workers involved stood up for me, after I was let go, and told HR and my management that I did not do what I was accused of. Then they told the unemployment office this same lie and even added to it by saying that I ADMITTED to what they accused me of doing!! I am just beside myself in disgust and disbelief. Isn't that slander? Can they lie to UI like that? Can I sue for something like this?