Is it possible to navigate to a parent directory in the jupyter tree?

As explained in https://github.com/ipython/ipython/issues/7751, it is not possible to navigate to the parent directory for security reasons:

The kernel might not be python, nor on the same machine than the server, nor do you need a running kernel to use server API(s).

If you want, you can ask for more information in the aforementioned GitHub issue.