I don't think either of you know what you want! You say that YOU split with her but you say that you still love her. Do you love her but know that it won't work between you, or were you not sure of your feelings with her when you broke up? If it's the former, it's hard, but you have to try and make a clean break. If it's the latter, but now you realize that you DO love her, then you should tell her and see if there's any chance of trying things again.
I think it's POSSIBLE that she's manipulating you and trying to make you jealous... do you know if this person at work thinks that they're in a relationship? If so, then it would appear she's telling the truth. If it's possibly not true, then you need to be open about your feelings. IE "I feel jealous to see you moving on but we shouldn't get back together because the same problems are still there", or "I realize now that I really do love you and want to try again", or even "I really don't know what I want". That's OK - but be HONEST about it!
Good luck!
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