I've been appointed as product owner of an application.
Within the organization, someone has positional power over you and the business analyst. It may be worth getting this person - your manager and the business analyst's manager, if they aren't the same person - involved in a conversation about roles and responsibilities. This would include both a clear understanding of your role, responsibilities, accountabilities, and authority on the product or project, but also that of the business analyst.
I have a good understanding of we need and how to achieve it. So I
jump wherever I see I can contribute to achieve the goal.
Usually that is some technical stuff even if I'm not the technical
leader (the project is related with big data analysis)
When you're in a leadership position, sometimes jumping in is the wrong thing to do. Sometimes, it's not only not jumping in, but also saying no and making sure that the people with specific roles and responsibilities around move the team closer to achieving the goal.
Although it's good that you are there and have the necessary skills and knowledge, leaders should empower the people around them. If people are genuinely stuck, find ways to convey your expertise and avoid doing the work - facilitate, teach, and partner up rather than doing work beyond product management as much as possible. It may also be good to wait to be asked rather than jumping in.
I'd also question how time is spent. If you're jumping in to help with these things outside the core duties of a product owner, how are you also finding time to get product owner work done?
The business analyst is helping me when I ask, in defining some
concepts and whit some investigation.
However the business analyst started to contact stakeholders to define
the roadmap of the product, mapping features and capabilities....
which I realize is actually the PO job.
Work typically done by a product owner can be delegated. Although a product owner may be accountable for communicating with stakeholders and putting together roadmaps and backlogs, the product owner could delegate these things to someone else while remaining accountable. If the business analyst has skills and expertise in these things and sees you jumping in to contribute where you have skills and expertise, they could see this as an invitation to jump in and contribute to these.
I feel I'm losing my ownership, my leadership, as well as the project.
On the other side, my contribution is still perceived as important,
but rolewise, nobody understand who I am and what I am doing.
Based on everything else, it seems like you're either not asserting leadership or demonstrating behaviors that don't match what you want to see the rest of the team do. This is leading to the confusion.
I end up being a "crucial contributor"
There's nothing wrong with this. There's nothing wrong with a first-among-equals approach. In fact, I'd go so far as to suggest that this is a key component of self-organizing, self-managing teams. Anyone on the team can demonstrate leadership principles, especially by exerting expert power because of their expertise, skills, and training rather than power derived from their position in the organization.
