# I loose a question

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

Parallel transport as algebra isomorphism

Can one help my to find that conversation?

Thank you very much

• I have tried searching using this SEDE query for the word Douady in comments on your posts. The only question if found was Differential and pre-differential of Jacobi identity. (I did not find any mentioning Dixmier.) The same query on math.SE returns no results. (You can try other reasonable keywords.) May 6, 2017 at 7:27
• @MartinSleziak Thank you very much for your help. May 6, 2017 at 7:47
• But I guess that the question I linked to is not the one you are looking for, right? May 6, 2017 at 7:48
• @MartinSleziak Yes it is not but I thank you for showing me the explor data search system. My conversation was about obstructions for fiberwise matrix algebra structure for a vector bundle. May 6, 2017 at 7:50
• @MartinSleziak I remember that some one answered me Duaddy Diximier invariant (Or class) or some thing like this(In the third cohomology) May 6, 2017 at 7:52
• Are you sure it was spelled Diximier in those comments? (You have also used various spellings of Douady in your question and your comments here on meta.) May 6, 2017 at 7:55
• @MartinSleziak Yes you are right. My spelling was incorrect. Thanks :) May 6, 2017 at 10:02
• I can't help with finding the MO conversation, but indeed such bundles are governed by Dixmier-Douady characteristic classes in $H^3(X,\mathbb{Z})$. This is all discussed in Husemöller, Joachim, Jurco, Schottenloher "Basic Bundle Theory and K-Cohomology Invariants" (2008), more specifically in Chapter IV.
– M.G.
May 11, 2017 at 22:28
• @July I sincerely thank you very much for this reference. May 12, 2017 at 5:07