?? rep of clifford algebra of ["discriminant" quadratic form on binary quadratic forms] on k^2 given by isomorphism (?? ...) of clifford-jordan algebra to underlying jordan algebra of operators on k^2 ... ??? .....

?? tricky vs non-tricky aspects of left-universal properties involving jordan algebras ... ?? on input vs on output sides ... ???? .... ?? ...

?? hmm, sounds probably related to story about "integral spinors" that i used to know ...... ????? ....

?? trying to dredge up vague memory .... ??? relationship to "rationalness of the circle" ??? .... ???? ..... ??? ..........

?? ... ?? any relationship to a1 dynkin diagram coincidence ?? ... ?? .... ?? hmm, maybe yes ?? ... gl(2,2) as split quaternions ... ?? gets non-standard anti-involution here, with traceless as "imaginary" .... shift-gradedness of anticommutator wrt (?? ... fourier duality grading ...) anti-involution .... making imaginaries into anticommutator algebra .... ?? meanwhile traceless corresponding to symmetric ... so transport the anticommutator algebra across that bridge and ... ?? maybe that's the symplectic lie algebra structure on the symmetric bilinear forms ??? .... ???? .... ???? .... ?? "quadrant" picture of symplectic lie bracket here ??? ..... ???? .... ???? ...