Should an undergraduate claim ownership of their article uploaded on arXiv? As an undergraduate, I wrote a paper with a professor in the physics department. He has uploaded the paper to arXiv, and he forwarded me the email that he (automatically) received upon submitting the article. Part of it states:


  A paper password will be emailed to you when the article is announced. 
  You should share this with co-authors to allow them to claim ownership.


Does this mean that, even as an undergraduate, I should create an account on arXiv (not sure if possible) and claim co-ownership of the article?
Congratulations on your paper!

You don't have to, but it would be a good idea to make an arXiv account and use it to claim ownership of the paper.  This will make it easier for people to find your work when searching by your name, and vice versa.  It will also establish an account that you can use for any future papers you write.

The fact that you're an undergraduate is irrelevant; arXiv doesn't care.  In fact anybody at all can create an arXiv account.  In order to actually submit an article, there is an endorsement process, but that's not really important here: endorsement isn't needed to claim ownership of a paper submitted by someone else (and presumably your co-author is already endorsed).