The generalized Casimir operator
is the only known polynomial element of the center
of the universal enveloping
algebra
of an indefinite Kac–Moody algebra
. However, Kac [115
] has proven the existence of higher order
non-polynomial Casimir operators which are elements of the center
of a suitable completion
of the universal
enveloping algebra of
. Recently, an explicit physics-inspired construction was made, following [115], for affine
in terms
of Wilson loops for WZW-models [1].