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Bulletin of the London Mathematical Society Advance Access originally published online on August 24, 2009
Bulletin of the London Mathematical Society 2009 41(5):898-902; doi:10.1112/blms/bdp066
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© 2009 London Mathematical Society

Vector product algebras

Erik Darpö

Department of Mathematics
Uppsala University
Box 480
S-75106 Uppsala
Sweden

Received 10 October 2008. Revision received 13 March 2009.

Vector products can be defined on spaces of dimensions 0, 1, 3 and 7 only, and their isomorphism types are determined entirely by their adherent symmetric bilinear forms. We present a short and elementary proof for this classical result.

2000 Mathematics Subject Classification 17A30 (primary), 17A75 (secondary).


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