Wikipedia:Reference desk/Archives/Mathematics/2016 April 21
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April 21
editRepresenting the exterior algebra
editIs it possible to represent the exterior algebra of given dimension using a matrix basis, where the exterior product is computed by matrix multiplication? I'm guessing that it isn't, but I'm not too sure.--Leon (talk) 18:11, 21 April 2016 (UTC)
- Any associative algebra has a representation using itself as a module. The exterior algebra has a unit so the representation is faithful and you can turn it into a matrix representation by choosing a basis. I'm assuming you're talking about the exterior algebra of a vector space, not sure about generalizations. --RDBury (talk) 23:29, 21 April 2016 (UTC)