In physics textbooks one frequently sees the name (affine) Kac Moody algebra used to describe the universal (one dimensional) central extension of the loop algebra of a semisimple algebra. But this is not an affine Kac Moody algebra: one would still need a derivation extension to obtain a true (untwisted) affine Kac Moody algebra.

Do the properties of the object that physicists call affine Kac Moody algebra resemble the properties of the true Kac Moody algebra so closely that this misuse of the terms is rendered harmless? Meaning, are physicists somehow justified to assume that properties proved for affine Kac Moody algebras hold for "their" affine Kac Moody algebras?