I found on Wikipedia a generalization of 3D cross product which is a multilinear map that in N-D links an N-1-tuple of vectors to a vector which is orthogonal to all the previous one. I found that in this site there are some discussion about it Cross product in > 3d
Unfortunately both the article and the discussion above do not contain a citation for these results. Can you please tell me where I can find an open source publication that treats this topic? It could seem impossible but I haven't managed to find it anywhere yet.