I recently finished my PhD and moved on to a postdoc research position in a semi-related subject area at a different University. I have an idea for a narritive review in my old subject area and I have some time to make a start on it before the current project gets really busy.
My issue is that I would like to invite my old PhD supervisor and another researcher from a third University, who we have collaborated with before, to co-author the paper with me as they are experts in the area that the review would cover. My current postdoc supervisor/line manager and other research colleague do not have any expertise in this subject area.
Is it ok to start writing the paper with my old colleagues without permission or notification of my current research team/boss? Or should I tell them that I am writing a paper with my old colleagues, without being able to offer them the chance to be involved? Not sure what the expectation is and don't want to annoy anyone at my (very new) job.