I don't think your title matched what you're talking about but I'm going to address both.

1. Can cats have a broken heart? Answer: Yes. Many moons ago, I was working 6 days a week, 18 hours a day. My cat was depressed. I took her to the vet and that's what he told me. He gave her a shot of Vitamin B12 and told me that I had 2 choices. 1. work less hours cuz my cat was missing me. or 2. get a 2nd cat. Well I did both within a couple of weeks. The Vitamin B12 shot worked almost immediately btw. It took quite a long time for my cat to accept the 2nd one but eventually did. No more depression.

2. Can a cat get jealous? Answer: Yes. I have 2 different cats now. The 2nd one I got is sooooo jealous of the 1st cat and any attention that I pay to him. If the first cat is lying down with me, the 2nd one will come and bite the first so that he leaves and the 2nd cat will take the position that the 1st cat was in.

Summary: A cat can get jealous and/or a broken heart.