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Nov 19, 2010 at 4:23 comment added Aaron Meyerowitz Also, The $\bullet$ multiplication is the same as ordinary multiplication for matrices which commute (such as powers of one matrix) so a single matrix can only generate a dimension 3 subspace.
Nov 19, 2010 at 1:08 comment added Mariano Suárez-Álvarez The algebra cannot be generated by one element because a Jordan algebra is power-associative, and your algebra is not associative.
Nov 18, 2010 at 21:49 vote accept TOM
Nov 18, 2010 at 20:46 history answered Andrei Moroianu CC BY-SA 2.5