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A cross product is possible in a $3$D and in a $7$D system. What prevents a cross product from being possible in a vector system of higher number of dimensions? For instance $15$D or $2^n$$-1$ dimensions?

Allyn Shell
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    Possible duplicate of http://math.stackexchange.com/questions/1615341/higher-dimensional-cross-product, http://math.stackexchange.com/questions/706011/why-is-cross-product-only-defined-in-3-and-7-dimensions, http://math.stackexchange.com/questions/185991/is-the-vector-cross-product-only-defined-for-3d – Martin R Feb 25 '16 at 18:37
  • check out Hurwitz's Theorem and this paper by Massey – costrom Feb 25 '16 at 18:38
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    This is definitely not a duplicate of the cited question. It is quite clear that the OP is talking about a binary product because he/she talks about dimensions 3 and 7, where the quaternions and octonions provide a suitable binary product. See the links in costrom's comment. I think that was a very ill-informed closure. – Rob Arthan Feb 25 '16 at 18:49
  • this question is more likely a duplicate of http://math.stackexchange.com/questions/706011/, not the question actually cited above. The question linked here was also marked duplicate and closed, but may have more valuable information. – costrom Feb 25 '16 at 21:46
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    @costrom: thanks, I agree that the question you cite provides an answer to this one. I think it's a bad idea for questions to be closed as duplicates with an incorrect justification. – Rob Arthan Feb 25 '16 at 22:38

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