According to http://arxiv.org/abs/0812.2690, real Lie algebras whose
max compact subalgebra has a u(1) factor should be called "conformal
Lie algebras", and are important in AdS/CFT (basically u(1) are
dilatations in the z direction (UV/IR)). These algebras are su(m,n)
(only if m=n??), so(n,2), sp(n, R), so*(2n), E_{7,-25}.
According to http://arxiv.org/abs/0812.2690, real Lie algebras whose max compact subalgebra has a u(1) factor should be called "conformal Lie algebras", and are important in AdS/CFT (basically u(1) are dilatations in the z direction (UV/IR)). These algebras are su(m,n) (only if m=n??), so(n,2), sp(n, R), so*(2n), E_{7,-25}.