I have attempted to google for this, but the searching is marred by the close relationship of Jordan Algebras and Quantum Mechanics. I have been passively thinking of this question for ages, tonight I finally post it. :)
My question is fairly simple. Similar to the universal enveloping algebra for Lie algebras, we should be able to form a universal enveloping algebra for Jordan algebras. So question one:
Can we indeed construct this "Universal enveloping algebra"?(Thanks Matt)
We can form a Universal enveloping algebra for Jordan algebras. So;
Are there some sort of Serre relations for Jordan algebras?
and then as we do for Lie algebras,
Can we find "quantum Jordan 'Serre' relations" for quantum Jordan algebras?
Can we deform the Jordan Universal Enveloping algebra in a similar way that we deform Lie Enveloping algebras to their quantized versions?
I would be happy with an explanation or a reference.
Thanks in advance!