?? map taking

a b
c d

to

b -a
d -c

, exchanging (...) traceless with symmetric ... ?? as a complex structure ??? ..... ????? ......

???? su(1,1) here somewhere ????? .... ????? .....

?? or u(1,1) ... ?? quaternions as 2d rep of u(2) ... ?? split quaternions as 2d rep of u(1,1) ??? ... ?? .....