can formally be written as an infinite sum of elements of formula_12. infinite series may or may not converge, so it need not define an actual element "Z" in formula_12. For many applications, the mere assurance of the existence of this formal expression is sufficient, and an explicit expression for this infinite sum is not needed. This is for instance the case in the Lorentzian construction of a Lie group representation from a Lie algebra representation. Existence can be seen as follows.