I remember that I had asked a question about obstructions for a $n^2$ dimensional vector bundle for which the fibers admit a structure of matrix algebra. I do not remember whether it was an independent question or it was included in comments in another question.
I searched a lot both in web and in Mo to find that question but I can not find it. I remember a participant says that there are obstructions as Diximier Duady classes in 3th cohohomology of the base space.
I would like to read that conversation as a supplementary to the following my MO question
Can one help my to find that conversation?
Thank you very much