Can you be more specific? That's like asking "what math do I need to understand quantum mechanics".... as with any such question, it depends on how deeply you want to understand it.
Perhaps you might start with a paper you don't understand, or terminology that you recognise comes from algebra but aren't familiar enough with to make sense of the paper.
As asked, I think the answer to your question is analysis and algebra. A Master's degree should suffice.
