My paper with Alex and Matthew summarizes some of the relevant ones. The early chapters of Faraut and Koranyi’s book Analysis on Symmetric Cones are a good reference; the Wikipedia article on Symmetric Cones seems to be based on it.

For general mathematical interest, Kevin McCrimmon has a nice general intro article on Jordan algebras, but has less of the relevant detail, and goes relatively quickly into Jordan algebras over arbitrary fields.

I suspect quaternionic vs. complex may not make much difference to QMA(2)-type classes, since the peculiarities of quaternionic composites seem more relevant to cryptographic issues of the sort that might arise with multiple provers, than to the complexity of determining separability vs entanglement, which seems most relevant to QMA(2).

]]>Thanks for your comments. Do you know a good online introduction to Jordan algebra?

]]>